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QUALITATIVE ANALYSIS OF PARTICULATE SYSTEMS by Sang Hoe Koo A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Com puter Science) August 1994 Copyright 1994 Sang Hoe Koo U M I Number: DP22885 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Pub! shmg UMI DP22885 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106- 1346 UNIVERSITY OF SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CALIFORNIA 90007 This dissertation, w ritten by SA-A/& tfoBr k io O under the direction of h Dissertation Committee, and approved by all its members, has been presented to and accepted by The Graduate School, in partial fulfillm ent of re quirem ents for the degree of D O C TO R OF PH ILOSOPH Y Dean of Graduate Studies Date DISSERTATION COMMITTEE Chairperson P h . P . cps Acknowledgem ents I thank: Shankar Rajamoney, m y advisor, for providing the opportunity to conduct this research, for providing a constant source of ideas and fruitful discus sions and for providing an intellectually stim ulating research environm ent. Ari Requicha and Behrokh Khoshnevis for serving on m y dissertation com m ittee and for m any helpful suggestions and advice on the thesis. Paul Rosenbloom, Ram Nevatia, and D an M oldovan for serving on m y qualifying exam comm ittee and for helpful discussions and criticisms. Prasanta Bose, Hee-Youn Lee, Nicolas Rouquette, and Sungdon Cho, the m em bers of the qualitative reasoning group, for useful discussions and helpful suggestions on this research. Sungbok Kim, Soowon Lee, Joungw oo Kim, Jihie Kim, June Park, Junghyun H an, and Youngwoo Choi for their m any interesting discussions and en couragem ent. Contents A cknowledgem ents ii List O f Tables vi List Of Figures vii Abstract x 1 Introduction 1 1.1 Qualitative P h y sics...................................................................................... 1 1.2 Qualitative. Reasoning about Particulate S y ste m s................................ 4 1.3 A n Application Involving Particulate S y s t e m s .................................. 6 1.3.1 A n E x a m p le ................................................................................... 6 1.4 Research Is s u e s ............................................................................................. 8 1.5 Examples of Particulate S y s te m s ............................................................ 8 1.6 Thesis C o n trib u tio n s................................................................................... 11 1.7 Thesis O rg a n iz a tio n ................................................................................... 12 2 The PA/AI O ntology 14 2.1 Existing Ontologies ................................................................................... 15 2.1.1 The Device O n to lo g y ................................................................... 15 2.1.2 The Contained-Liquid O n to lo g y ............................................... 17 2.1.3 The Piece-of-Stuff Ontology ...................................................... 18 2.1.4 Limitations of Existing O n to lo g ie s............................................ 19 2.2 M odeling Particulate S ystem s................................................................... 20 2.2.1 Population-centered M o d e lin g .................................................. 22 2.2.2 The PA /A I O n to lo g y ................................................................... 25 2.3 Discussion ................................................................................................... 27 3 Representation of Particle Aggregates and Aggregate Interactions 29 3.1 P S /IP N e tw o rk ............................................................................................. 29 3.2 Representing Particle A ggregates and Aggregate Interactions . . . 31 iii 3.2.1 P re lim in aries.................................................................................... 31 3.2.2 Particle A g g re g a te s ....................................................................... 32 3.2.3 Aggregate Interactions ................................................................ 34 3.3 Discussion .................................................................................................... 38 4 PA Identification M ethod 39 4.1 Interaction-D riven Particle C la s sific a tio n ............................................ 40 4.2 G enerating R elations................................................................................... 41 4.2.1 Characteristics of Interactions ................................................... 41 4.2.2 Types of R e la tio n s .......................................................................... 44 4.3 The PAI M e t h o d .......................................................................................... 50 4.4 Discussion ................................................................................................... 54 5 M odeling and Sim ulation 56 5.1 QP T h e o r y ................................................................................................... 56 5.2 M odeling P A /A I .......................................................................................... 57 5.2.1 Particle A g g r e g a te s ...................................................................... 58 5.2.2 Aggregate Interactions ................................................................ 60 5.3 M odeling Kinetic Energy R ed istrib u tio n ............................................... 61 5.4 M odeling Interconnecting Theories ...................................................... 63 5.5 Sim ulation ................................................................................................... 65 5.6 A dditional Sim ulation E x a m p le s............................................................ 65 5.7 Discussion ................................................................................................... 68 6 Related Work 70 6.1 Ontologies ................................................................................................... 70 6.2 Particulate Systems ................................................................................... 72 6.3 M ultiple M o d e ls ......................................................................................... 73 6.4 A g g r e g a tio n ................................................................................................ 74 6.5 Discussion ................................................................................................... 75 7 Evaluation 77 7.1 The Chem istry D o m a in ....................... 77 7.2 O ther D o m a in s ............................................................................................. 87 7.2.1 The Electronics D o m a in .............................................................. 87 7.2.2 The Economics D o m a in .............................................................. 89 7.2.3 The Biology D o m a in ..................................................................... 91 7.3 Discussion ................................................................................................... 93 8 D iscussion 95 8.1 S u m m a ry ....................................................................................................... 95 8.2 Future R e s e a r c h ......................................................................................... 96 8.3 Significance of the R esearch ...................................................................... 97 iv Appendix A Details of the Escape Example ........................................................................ 98 A .l The PAI M e t h o d ........................................................................................ 99 A. 1.1 System I n p u t s ............................................................................... 99 A.1.2 PA Id en tificatio n ...............................................................................100 A. 1.3 System O u tp u t.................................................................................. 101 A.2 QPE Simulation ........................................................................................... 102 A.2.1 System I n p u t s .................................................................................. 102 A.2.2 System O u tp u t.................................................................................. 108 Appendix B Sum m ary of E x am p les............................................................................................112 B.l Exam ples from the Chem istry Dom ain .................................................112 B.2 Exam ples from O ther D o m a in s.................................................................114 v List Of Tables 3.1 (a) Three particle aggregate model, (b) Scenario description of contained water, (c) Its particle aggregate instances........................... 35 3.2 A m odel for aggregate interaction escape.............................................. 37 4.1 Types of relations for classified particles................................................ 45 4.2 Two algorithm s for the PAI m ethod and IDPC..................................... 51 5.1 (a) The individual view definition for the particle-aggregates in therm odynam ic particulate systems, (b) The scenario description for particle aggregates identified by the PAI m ethod, (c) Parti cle aggregate instances generated, (d) Aggregate relationships betw een the particle aggregates................................................................ 59 5.2 A process definition for the interaction escape.................................... 60 5.3 M odels of kinetic energy redistribution w hich includes (a) a m odel to m ake tw o particle aggregates of high and low kinetic energy coexist, and (b) redistributory com pensation processes to keep them coexistent.............................................................................................. 62 5.4 The interconnecting theory corresponding to the entity contained- liq u id ............................................................................................................... 64 7.1 The coverage of exam ple problem s in the chem istry dom ain. Ex am ples are borrow ed from College Chemistry by Bruce H. Mahan (1966)................................................................................................................ 78 B.l The sum m ary of sim ulations on the exam ples from the chem istry dom ain................................................................................................................112 B.2 The sum m ary of sim ulations on the exam ples from the chem istry dom ain (continued).........................................................................................113 B.3 The sum m ary of sim ulations on the exam ples from other dom ains. 114 vi List Of Figures 1.1 The qualitative sim ulation of a m ass-spring m odel. Given a do m ain m odel and a structural description, the sim ulator first gen erates the causal netw ork for the situation, and then com putes the behavior of the system w ith the netw ork............................................... 2 1.2 Schematic diagram for qualitative reasoning. Given a physical system and a query, a hum an m odeler builds the dom ain m odel and the system m odel suitable for the query. Then, the qualitative reasoner analyzes the physical system using the dom ain m odel and the system m odel to provide an answ er to the q u e r y .............. 3 1.3 A m otivating exam ple of particle escape. As w ater particles es cape into surrounding atm osphere, the am ount and tem perature of the rem aining solution decrease.......................................................... 7 1.4 Situations involving particulate systems, (a) A contained solution consisting of salt dissolved in water, (b) A chem ical reaction. (c) The electrolysis of water, (d) A sodium -potassium pum p model. 9 2.1 A N avy Propulsion plant: w ater from the sea is pum ped into the boiler and boiled to generate steam. The steam is heated at the superheater and supplied to the engine, (a) The device model. (b) The contained-liquid model, (c) The piece-of-stuff model. . . . 16 2.2 Exam ple queries on a particulate system, a contained solution of w ater and salt................................................................................................ 20 2.3 M odeling contained solution for various queries................................ 21 2.4 The population-centered m odels for contained solution for vari ous queries...................................................................................................... 24 2.5 (a) A P A /A I m odel for particle escape in a particulate system (the ovals represent particle aggregates). Here, the particle aggregate of w ater particles are divided into particle aggregates of high and low kinetic energy particles, (b) The part-w hole relations that hold betw een the particle aggregates...................................................... 26 2.6 Different m odels for the same particulate system , (a) A m odel for a query about ionization, (b) A m odel for a query about evaporation. 27 vii For a sim ple physical system of solution w ith salt dissolved in w a ter, the dom ain m odel m ay include theories on various interactions. 30 P S /IP netw orks for the exam ples in Figure 2.6. By superim posing the netw ork over the particulate system, w e can choose m odels for the physical system that are relevant to the given query. ... . 31 Particle classification of the contained-w ater example: the parti cles in a container is initially m odeled by a single PA (1). W hen we consider the interaction escape w e classify particles in it to form tw o particle aggregates according to their kinetic energy (2 an d 3). 41 W hen an interaction particle escape is potentially active in liquid particles, IDPC classifies the particles in the liquid particle aggre gate to form high and low kinetic energy particle aggregates. For these new ly generated particle aggregates, some relations are im posed, such as part-w hole, p art-part and part-interaction relations. 42 Three exam ples that illustrate characteristics of interactions: (a) escape, (b) capture and (c) vaporization................................................. 44 For the exam ple of contained w ater involving escape and freeze, IDPC divides the w ater particle aggregate into four particle aggre gates. For these particle aggregates, relations are generated and added to the m odel instances of particle aggregates and aggregate interactions accordingly............................................................................. 49 The P-I diagram generated for the contained-w ater exam ple. In this figure, pn is a particle aggregate, PS-a and PS-v are particle system s for contained-w ater and vapors, I and g m ean the phases of pn's, nam ely liquid and gas, and (11,12) is the interval for kinetic energy. ......................................................................................................... 53 According to M axwell's distribution, it is not physically possible that low kinetic energy particles rem ain w hen all the high kinetic energy particles escape into atm osphere................................................ 61 A sim ulation exam ple for particle escape in the contained w ater (See Figure 1.3). An explanation for the tem perature drop is given. 66 Two additional sim ulation examples, (a) Evaporation rate drop in solution (Figure 1.4(a)), and (b) the reaction rate increase due to heating (Figure 1.4(b))............................................................................. 67 (a) Situations involving phase transitions, (b) Q ualitatively im portant particle aggregates identified by the PAI m ethods, (c) Explanations for various queries.............................................................. 81 (a) Situations involving chemical reactions, (b) Q ualitatively im portant particle aggregates identified by the PAI m ethods, (c) Explanations for various queries.............................................................. 83 7.3 A situation involving electrolysis, (a) A n electrolysis of H 2O. (b) Particle aggregates and potentially active aggregate interactions identified by the PAI m ethod, (c) A n explanation for the appear ance of hydrogen gas at the cathode........................................................ 85 7.4 A situation involving gaseous diffusion, (a) Gaseous diffusion of hydrogen and nitrogen, (b) Particle aggregates identified by the PAI m ethod, (c) A n explanation for the pressure difference betw een the tw o cham bers......................................................................... 86 7.5 (a) A variable capacitor, (b) Particle aggregates identified by the PAI m ethod, (c) A n explanation of the increase in charge w hen the capacitor is being closed....................................................................... 88 7.6 (a) D em and schedule, (b) Particle aggregates identified by the PAI m ethod, (c) A n explanation of the increase in quantity purchased w hen the price of the product is decreasing.......................................... 90 7.7 (a) The potassium -sodium pum p model, (b) Particle aggregates and aggregate interactions identified by the PAI m ethod, (c) A n explanation of the increase in concentration of potassium ions (K+) inside cells............................................................................................. 92 ix Abstract For applications such as intelligent tutoring system s that im part advanced sci entific concepts or expert system s that base their conclusions on causal theories, a deeper understanding of the physical phenom ena u n d er study (e.g. chemical reactions and the factors influencing them , the functioning of transistors, the functioning of a living cell, or everyday phenom ena such as evaporation and diffusion) is required. This deeper understanding typically requires reasoning about the particles constituting the physical systems. We call such system s partic ulate systems, and this thesis investigates how to qualitatively analyze particulate systems. C urrent qualitative reasoning m ethods are inadequate for representing and reasoning about particulate system s since there are so m any particles and the behavior of individual particles is irregular and transitory. In this thesis, w e m ake an im portant observation that regular patterns of behavior em erge over aggregates of particles, and these behavioral patterns are critical for reasoning about particulate systems. We show how to identify particle aggregates that are relevant and useful in reasoning processes. O ur m ethod, called the PAI m ethod, finds relevant particle aggregates and their qualitative relationships based on w hether they participate or not in interactions. Based on this m ethod, w e intro duce an ontology, called the PA /A I ontology, in w hich a particulate system is m odeled as a collection of particle aggregates and aggregate interactions. This ontology facilitates hum an m odeling of particulate systems. Then, w e show how particulate system s m ay be m odeled using this ontology, how their m odels m ay be represented in QP theory [Forbus 1984], and how QPE [Forbus 1989] m ay be used to sim ulate and build explanations for various physical phenom ena. The fram ew ork has been im plem ented and dem onstrated on m any dom ains. We have analyzed a college-level chem istry textbook, COLLEGE CHEMISTRY [M ahan 1966], to estim ate the coverage of exam ples by our system . We found that about 50% of the exam ples in the text are of particulate system s and out of the 50%, about 70% can be handled b y our system. We discuss lim itations of the system that prevent it from analyzing the remainder. Furtherm ore, w e have selected three different dom ains: biology, electronics and economics, and dem onstrated the m ethod on representative exam ples from these dom ains. Chapter 1 Introduction 1.1 Qualitative Physics Qualitative physics, a subfield of AI, is concerned w ith understanding physical system s. Qualitative reasoning is a m odel-based reasoning m ethod in w hich a dom ain m odel describing the objects in a dom ain and their interactions is used to reason from first-principles about a given physical system. Qualitative simulation is a form of qualitative reasoning in w hich the qualitative behavior of a physical system is determ ined from its structural description and a dom ain m odel. In this reasoning m ethod, the objects in the physical system are replaced by their m odels, and the physical laws governing their interactions are applied. Figure 1.1 describes the qualitative sim ulation of a sim ple m ass-spring sys tem. The dom ain m odel (Figure 1.1(a)) describes objects such as a spring and a mass. The m odel for a spring describes param eters such as length, rest-length and elasticity, and causal relations betw een these param eters such as the restor ing force is inversely proportional to the difference betw een the spring's length and rest-length. The m odel for a m ass object includes param eters such as posi tion, velocity and acceleration, and causal relations such as the acceleration is the derivative of the velocity, and the velocity is the derivative of the position. In the given physical system (Figure 1.1(b)), there is a spring (S) attached to a m ass (M). By applying the dom ain m odel to the structural description, a causal netw ork 1 (a) Domain model (b) System model External Force — Length, RL, Elasticity Elasticity ~ Q (Length - RL) , Pos, Vel, Acc V ---------------- 1+ [Pos, Vel] J (d) Qualitative behavior I h m p -T Length(S) = Pos(M) Acc(M) ocq Elasticity(S) M ------------£ .V..... Qualitative Simulator (c) Causal network / cc(M) Elasticity(S) Vei(M) Pos(M) :(M) V ‘ Length(S) Stretched At-rest-length V = +,stdj Compressed Figure 1.1: The qualitative sim ulation of a m ass-spring model. G iven a dom ain m odel and a structural description, the sim ulator first generates the causal net w ork for the situation, and then com putes the behavior of the system w ith the netw ork. (Figure 1.1(c)) is form ed from w hich the qualitative behavior (Figure 1.1(d)) is com puted. W hen an external force stretches and releases M, m ass M accelerates due to the elasticity of spring S [Acc(M) Q+ Elasticity(S)], w hich results in an increase in its velocity [1+ (Vel(M), Acc(M))], and a change of its position tow ards the wall [Pos(M) Q+ Vel(M)]. This continues until M m oves to a position w here the length and the rest-length of S are the same, at w hich tim e the direction of acceleration reverses. This propagation through the causal netw ork is repeated to generate the oscillatory behavior of m ass M. Q ualitative reasoning m ay be partitioned into tw o broad areas: modeling and reasoning[24]. Given a query (or a set of queries) about a physical system , the m odeling task is to utilize the dom ain know ledge to build a m odel w hich 2 Domain Model Physical System System Model Query ^Dom ain' Knowledgi Qualitative Analysis Qualitative Reasoner Modeler (human) Figure 1.2: Schematic diagram for qualitative reasoning. Given a physical system and a query, a hum an m odeler builds the dom ain m odel and the system m odel suitable for the query. Then, the qualitative reasoner analyzes the physical system using the dom ain m odel and the system m odel to provide an answ er to the query. contains the know ledge needed to analyze the system , and to determ ine an idealized m odel of the physical system that is suitable for answ ering the query. Modeling is a complex task that is usually perform ed by hum an m odelers. It includes: (a) selecting suitable ontological prim itives (that is, determ ining w hich objects of the system and their properties are relevant to the analysis), and (b) selecting a suitable level of abstraction (e.g. if the system m odel contains too m uch detail, the analysis becomes inefficient and, sometimes, intractable; if the m odel is too abstract, it m ay fail to provide an answ er to the query). Reasoning includes the representation of the dom ain and system m odels (based on the selected ontological prim itives), and reasoning w ith these m odels. For representation, a language describing the objects and their interactions is required. For reasoning, algorithm s that operate on the representation to draw inferences about the given physical system m ust be developed (See Figure 1.2). Three representations and associated qualitative reasoning algorithm s have been developed and intensively studied. De Kleer and Brown[10] use a device- centered representation to m odel physical system s, and their ENVISION pro gram com putes the qualitative behavior. Kuipers[24] uses qualitative differen tial equations to m odel physical system s, and his QSIM program determ ines 3 the qualitative behavior. Forbus[17, 15] uses a process-centered representation to m odel physical systems, and his QPE program determ ines the qualitative behavior. Q ualitative physics is useful in the analysis of system s for w hich precise physical or num erical inform ation is not available, or w hen, even if exact in form ation is available, the reasoning is expensive. Consider w hat w e need to know about the physical w orld to m ake coffee[16]. We know that to pour coffee from a pot into a cup requires having the cup under the spout of the kettle, and that if w e pour too m uch in, there will be a m ess on the floor. We know all this w ithout the precise equations required by traditional physics to m odel the situation. Q ualitative physics is useful in representing and reasoning about such situations. In practical applications such as design and diagnosis, qualitative reasoning m ay provide useful prelim inary results. In a design task, prelim inary analysis of the desired behavior and the qualitative m odels of com ponents m ay suggest a set of alternative partial designs. Then, detailed analysis m ay generate a practical design solution w ith reduced effort. In a diagnostic system , qualitative analysis m ay detect significant deviations from norm al behavior, and m ay suggest a set of diagnostic hypotheses w hich m ay be further analyzed w ith m ore accurate, quantitative inform ation[8]. Qualitative reasoning has been applied to a broad range of tasks including diagnosis[18, 8, 11], design[5, 19], intelligent tutoring systems[14], and planning[21], and in a rich variety of dom ains (e.g. physics[15], chem istry[30], biology[22], system dynamics[4], and electronics[9]). 1.2 Qualitative Reasoning about Particulate Systems W hile conventional qualitative reasoning system s dem onstrate perform ance, the explanations they provide are often inadequate because their dom ain m odels are not sufficiently expressive. Often, qualitative reasoning based on the causal 4 m odels of constituent particles plays a central role in the deeper understand ing of m any physical mechanism s. Examples include understanding chem ical reactions and the factors influencing them , the functioning of a living cell, and everyday phenom ena such as evaporation and diffusion. Detailed reasoning about such system s is useful in m any application fields such as intelligent tutor ing system s for chem istry and biology, diagnostic system s for electronic devices, and design system s for therm odynam ic devices. In this thesis, w e address the problem of understanding qualitatively the behavior of a class of physical sys tem s w hich w e call particulate systems. Particulate system s are a class of physical system s w hich display the follow ing characteristics: 1. The system is com posed of a large num ber of objects (which w e call par ticles) such that m odeling all of the individual objects in the system is com putationally infeasible. 2. The behavior of individual particles is irregular and does n o t facilitate reasoning about the behavior of the system as a whole. 3. The behavior of each particle is transitory in that its duration is negligibly short com pared w ith the duration of the overall system 's behavior. 4. Yet, the behavior of aggregates of particles follows a p attern that is not large in num ber, irregular, or transitory. C urrent qualitative reasoning m ethods are not suited for the representation and reasoning of particles, nor can they be readily adapted for such purposes. The determ ination of the individual behavior of billions of particles is im pos sible; and, even if it w ere possible, it is useless since the behavior lasts less than a billionth of a second. Consequently, the m ost im portant requirem ent for analyzing particulate system s is to capture the patterns of behaviors of particle aggregates. 5 1.3 An Application Involving Particulate Systems In this section, w e dem onstrate how qualitative analysis of particulate system s is of practical use in an application, an intelligent tutoring system for chemistry. One-to-one tutoring is one of the m ost effective educational delivery m eth ods. A com putational education tool that can replicate the one-to-one tutor ing m ethod is an intelligent tutoring system (ITS). A n ITS involves 3 m ajor processes[43]: constructing m odels of the dom ain to be taught, constructing the student's m ental m odels of his understanding of the dom ain, and planning com m unications betw een the system and the student for effective know ledge transfer. Two w ell-know n problem s of past ITS systems[43] are: (1) A lack of a qualitative description of dom ain m odels. W ith quantitative m odels of a dom ain, the system can not help students w ith m isunderstandings because the students' cognitive m odels of a dom ain are usually qualitative. (2) A lack of m ultiple m od eling capabilities for a dom ain. With a single m odel of a dom ain, the system can not help students because students' m ental m odels advance from a superficial m odel to an in-depth m odel as their m astery of the dom ain progresses. 1.3.1 An Example C onsider the following query: Why does the temperature of the solution of water and salt in the open container drop? (Figure 1.3) A n ITS, using a sim ple m odel of evaporation, should answer: The contained solution is exposed to the external atm osphere; conse quently, the w ater in the solution evaporates. Evaporation leads to the drop in the tem perature of the solution. If the student further asks why evaporation causes the tem perature to de crease, then the ITS, using deeper causal m odels of the constituent particles of the solution, should answer: 6 Solution temperature (Solution) 1 1 - amount (Solution) 1 1 Figure 1.3: A m otivating exam ple of particle escape. As w ater particles escape into surrounding atm osphere, the am ount and tem perature of the rem aining solution decrease. The solution is com posed of w ater and salt particles. The kinetic theory of fluids [25] postulates that the particles contained in the open container are continually in random m otion, and are held together b y interm olecular attractive forces of attraction. A m ong the w ater particles of the solution in the container, some have sufficient high kinetic energy to conquer the interm olecular forces, and som e do not. The particles w ith high kinetic energy m ay escape into the surrounding atm osphere, thereby changing from a liquid particle to a gas particle. The constant loss of such high kinetic energy particles results in a decrease in the average kinetic energy and the population of the rem aining w ater particles. Since the tem perature of the solution is proportional to the average kinetic energy of the w ater particles, the tem perature drops. The above tw o answ ers can not be generated from a single uniform m odel, b u t require tw o separate m odels of the same system. Conventional qualitative physics[15] provides the first explanation successfully, b u t not the second one. O ur approach involves deeper causal theories of particles, and can generate the second explanation. 7 1.4 Research Issues To perform qualitative reasoning about particulate system s w e need ontologi cal prim itives1 to m odel particulate system s, a representation language for the prim itives, and a reasoning m ethod. For instance, for the exam ple described in the previous section, w e need ontological prim itives to m odel the aggregates of particles w ith kinetic energy greater than and less than the barrier energy2 and the interaction affecting these particle aggregates; a m ethod to find such relevant particle aggregates and to identify relationships betw een them ; a rep resentation language to describe the particle aggregates, interactions, an d the relationships betw een the particle aggregates and the contained solution; and, a reasoning m echanism that determ ines the behavior of the particle aggregates by sim ulating their interactions. The goal of this thesis is to provide such m odeling and reasoning m echanism s. Four im portant questions that this thesis attem pts to answ er are: 1. What are appropriate ontological primitives for modeling particulate systems? 2. Which particle aggregates are important? 3. How are particle aggregates and their interactions represented? 4. How to qualitatively model and represent particulate systems to perform simula tion on QPE[17]? 1.5 Examples of Particulate Systems In this section, w e describe several particulate system s, and show how reasoning about the particles in each system is used to answ er queries about the system . 1The primitives describing the relevant properties of relevant objects. 2Barrier-energy denotes the level of kinetic energy held by particles to conquer the inter molecular attractive forces.[28]. 8 Water particle T Salt particle C l, NO Cl NOC.'I Sofui ion (a) NO(g) + Cl2(g) -> NOCl(g) + CI(g) (b) Oxygen j = Battery Anode e Cathode Na+ -K PU M E Net passive diffusion Metabolic drive Net passive diffusion (c) (d) Figure 1.4: Situations involving particulate system s, (a) A contained solution consisting of salt dissolved in water, (b) A chem ical reaction, (c) The electrolysis of water, (d) A sodium -potassium pum p model. Exam ple 1: Why does the evaporation rate of a solution of salt and water drop? (Figure 1.4(a)) of m any escape sites by occupying a portion of the w ater's surface/ the rate of evaporation drops. Exam ple 2: Why does the rate of the chemical reaction increase with heating? (Figure 1.4(b)) According to the collision theory of chemical kinetics[25 ], w hen two reacting molecules w ith sufficient kinetic energy collide, they interact to produce 3 Liquid particles with kinetic energy greater than barrier energy. 4A solution consists of two components: solvent and solute. Evaporation is the escape of high kinetic energy liquid particles3 from the surface. Since in a solution, the solute4 particles deprive the solvent particles 9 new molecules. W hen the reacting molecules in the container are heated, the kinetic energy of the molecules inside increase. This results in an increase in the frequency of collisions and an increase in the num ber of molecules w ith sufficient kinetic energy; both these factors contribute to an increase in the rate of the chemical reaction. Example 3: Why does hydrogen gas appear at the cathode? (Figure 1.4(c)) If wires from a battery are connected to electrodes that dip into the water, w ater ionizes into hydrogen ion, H +, and oxygen ion, O2 -. W hen hydrogen ions hit the cathode, they gain electrons, e- , from the cathode to form hydrogen gas, H 2, and w hen oxygen ions hit the anode, they lose electrons to the anode to form oxygen gas. Example 4: How does the potassium-sodium pump model work? (Figure 1.4(d)) M aintaining low concentration of sodium, N a+, and high concentration of potassium, K+, inside cells is essential for generating nervous impulses[37] which are required for heartbeat. Biologists propose a sodium-potassium pum p model to explain how the concentrations are maintained. According to this model, a carrier substance, X, is assumed to combine w ith potas sium ions, K+, at the outer surface of the cell membrane, forming a new compound KX. KX then diffuses passively across the membrane following its own concentration gradient. At the inner surface of the membrane, KX dissociates, releasing potassium into the cell. X is immediately converted into another form, Y , by an energy-requiring reaction. Y combines w ith sodium ions, N a+, at the inner surface of the membrane, forming a new com pound NaY, which diffuses passively back across the m em brane to the outer surface along its own concentration gradient. At the outer surface, NaY dissociates, releasing sodium to the outside. Y is immediately con verted back into X, which can pick up a new load of potassium and start the process over again. As the working of the pum p causes the concentration gradient for sodium ions to become steeper and steeper, the net inw ard diffusion of these ions eventually equals the outward pum ping. Similarly, the net outflow of potassium falls to the point where it exactly balances the effects of the sodium-potassium pum p. A steady state that m aintains the concentrations of N a+ and K+ ions at their desired levels is reached. A part from these exam ples, other exam ples of particulate system s are: the functioning of a p-n junction in a diode, micro-economics, and the analysis of traffic patterns. 1.6 Thesis Contributions The m ajor thesis contributions are: 1. We develop tw o ontological primitives: particle aggregates (PA) and aggre gate interactions (AI) for m odeling particulate systems. 2. We develop the PAI (PA Identification) m ethod w hich finds the quali tatively im portant particle aggregates that are relevant to reasoning. Two subm ethods involved in the PAI m ethod are: IDPC (Interaction-D riven Par ticle Classification) w hich classifies particles in a particle aggregate along the landm arks5 of a quantity to distinguish interacting and non-interacting particles; PA relation generation m ethod w hich identifies relationships for the particle aggregates of the classified particles. 3. We develop a representation language for the ontological prim itives that facilitates reasoning about particulate systems. 4. We develop m odels for reasoning about particle aggregates, aggregate interactions, redistributory processes and interconnecting theories. We evaluate our fram ew ork by im plem enting exam ples from various d o m ains. We have investigated exam ples exhaustively from a college-level chem istry textbook, College Chemistry by Bruce H. Mahan (1966)[28], to find out the 5Landmarks are the specially designated values at which interactions become active or inac tive (e.g. freezing point or boiling point of water). 11 coverage of exam ples and im plem ented representative exam ples. Therefore, w e have found that about 50% of the exam ples are of particulate system s and out of the 50%, about 70% can be handled b y our m ethod. Furtherm ore, w e selected three different dom ains such as biology, electronics and economics, and have im plem ented several exam ples from them . Therefore, w e found th at our m ethod can be well applied to these dom ains. 1.7 Thesis Organization The rem ainder of this thesis is organized as follows: • In C hapter 2, w e discuss various ontologies developed in qualitative physics to m odel physical system s and show w hy they are not appropriate for m odeling particulate systems. Then w e describe tw o m odeling primitives: PA (particle aggregate) and AI (aggregate interaction) that are suitable for m odeling particulate systems. • In C hapter 3, w e describe the representation of particle aggregates and aggregate interactions. • In C hapter 4, w e describe the PAI m ethod w hich finds all qualitatively im portant and properly classified particles, and generates relationships of and betw een particle aggregates of classified particles. • In C hapter 5, w e describe how to m odel particle aggregates, aggregate in teractions, redistributory processes, and interconnecting theories using QP language[15], and show the sim ulation results for the selected examples. • In C hapter 6, w e discuss related w ork on qualitative reasoning, reasoning about particulate system s, and others. • In C hapter 7, w e evaluate this thesis w ork by perform ing sim ulations from various dom ains such as chemistry, electronics, biology and economics, then discuss limitations. 12 • In C hapter 8, w e review thesis contributions, and discuss the significance and future research. • In A ppendix A, w e describe the details of the sim ulation of particles escap ing from a contained liquid. • In A ppendix B, w e sum m arize the results of exam ples described in this thesis. 13 Chapter 2 The PA/AI Ontology Q ualitative reasoning involves (1) m odeling the given physical system by deter m ining the objects and their attributes relevant to its analysis, (2) developing a qualitative language to represent the m odel, and (3) determ ining the behavior of the physical system through qualitative sim ulation. The first task involves ontological commitment, and the types of objects w ith w hich the m odel is to be form ed are called ontological primitives or modeling primitives. Ontological com m itm ent should be relevant to the given physical system and the query regarding it. For exam ple, consider a m etal block. If the block is placed on a table and pushed, and w e ask how its position changes, then the block should be m odeled as a m ass w ith friction. If the block is connected at both ends to an electrical pow er source, and w e ask w hether an electric current flows through the block, it should be m odeled as a conductor w ith resistance. If the block is im m ersed in water, and w e ask how it m oves w hen pushed, it should be m odeled as a float w ith buoyancy. The ontological prim itives developed so far in qualitative physics are not suit able for the analysis of particulate system s w hich requires deeper understanding of the causal m echanism s of the constituent particles. In this chapter, w e review three w idely used ontologies for reasoning about physical system s developed previously in qualitative physics, discuss their lim itations for the analysis of particulate system s, and describe our PA /A I ontology that is novel and useful for the deeper analysis of particulate systems. 14 2.1 Existing Ontologies Three w idely used ontologies in qualitative physics are the device ontology [10, 44], the contained-liquid ontology[15,17] and the piece-of-stuff ontology[7]. 2.1.1 The Device Ontology In the device ontology[10, 44], a physical system is m odeled as a netw ork of devices. A device is described by a set of param eters, a set of causal relations betw een param eters that are im posed by the device, and a set of I /O ports. Consider the N avy Propulsion plant1 in Figure 2.1 in w hich w ater from the sea is p u m ped into the boiler and boiled to generate steam . The steam is heated at the superheater and is supplied to the engine. The device ontology m ay be used to m odel the system as a netw ork of devices such as a p u m p , boiler, and superheater. For exam ple, the superheater has I/O ports for steam , param eters such as flow rate, heat-transfer rate, and duration (the tim e the steam spends in the superheater), and causal relations betw een these param eters such as the duration of steam is qualitatively inversely proportional to the flow rate, and the heat-transfer rate is proportional to the duration (Figure 2.1 (a)). For a query: Given the tem perature of the w ater from the sea increases, w hat happens to the tem perature of the steam at the outlet? this ontology could be used to reason as follows: A t the boiler device, since the generation rate of steam is qualitatively inversely proportional to the difference of the tem perature of w ater from the boiling point, and the tem perature of the w ater is given to be increasing, the generation rate of steam also increases. Since the output of the boiler is the input of the superheater, flow rate of steam into the superheater device is increasing. A t the superheater device, lr rhis example is borrowed from [16]. 15 Pump (a) (b) water steam water steam Pumped- flow Steam- generation Heat-transfer Heat-transfer Heat- source Heat- source Sea Engine Super heater Pump Superheater Boiler Bui lei Steam (C) An MC pumped-flow boiling gas-flow heating Sea Boiler Boiler Superheater gas-flow Engine Figure 2.1: A N avy Propulsion plant: w ater from the sea is p u m p ed into the boiler and boiled to generate steam. The steam is heated at the superheater and supplied to the engine, (a) The device model, (b) The contained-liquid m odel, (c) The piece-of-stuff model. 16 since the duration of steam is qualitatively inversely proportional to the flow rate, and the heat-transfer rate is proportional to the duration, the heat-transfer to the steam decreases; consequently, steam w ith low er tem perature is supplied through the outlet. 2.1.2 The Contained-Liquid Ontology In the contained-liquid ontology[15,17], a physical system consisting of fluids is m odeled as fluids in containers w ith properties created by containm ent such as am ount. Interactions causing changes in the properties of fluids are m odeled as processes. Consider the N avy Propulsion plant (Figure 2.1). This system m ay be m od eled using the contained-liquid ontology as sea w ater contained in the sea and the boiler, and steam contained in the boiler, the superheater, and the engine. Physical processes such as pum ped-flow , steam -generation, heat-transfer, and gas-flow change the properties of these objects. For exam ple, gas-flow at the su perheater becom es active w hen there is a pressure difference betw een the boiler and the outlet, w hich decreases the am ount of steam in the boiler and increases the am ount of steam in the superheater. The heat-transfer in the superheater becom es active w hen steam exists in the superheater, and the tem perature of the steam is low er that the tem perature of the heat source, w hich increases the tem perature of the steam. The rate of heat-transfer qualitatively proportional to the duration of steam in the superheater, and the duration is qualitatively inversely proportional to the rate of gas-flow (Figure 2.1(b)). For a query: G iven that m ore steam is generated in the boiler, w hat h appens to the tem perature of the steam at the outlet? this ontology could be used to reason as follows: W hen the pow er plant is operating normally, processes such as steam - generation, gas-flow, and heat-transfer are active. The increase in the 17 am ount of steam in the boiler results in an increase in the pressure of the steam , w hich results in a larger pressure difference of steam be tw een the boiler and the outlet. Since the rate of gas-flow through the superheater is qualitatively proportional to the pressure difference, the rate of the process increases, hence the duration of the steam in the superheater decreases. Since the rate of heat-transfer at the su perheater is qualitatively proportional to the duration of steam in the superheater, less heat is transferred to the steam. Therefore, steam at low er tem perature is supplied to the engine. 2.1.3 The Piece-of-Stuff Ontology In the piece-of-stuff ontology[7], a system is m odeled as a collection of pieces, called m olecular collections (MC), and reasoning involves determ ining the path of the pieces through the physical system , and the changes to the MC at each com ponent on the path. Even if a physical system is in equilibrium state, several processes m ay be active, but, the com bined effect of all the processes m akes the system static. The piece-of-stuff is useful for reasoning about the internal activity in this equilibrium system . Reasoning about the m olecular collection is typically perform ed based on the results of reasoning at the contained-liquid ontology[7]. Consider the N aval Propulsion plant (Figure 2.1). This ontology m odels an MC in the system to reason about the path taken by a piece of w ater through the system and changes on the w ay (Figure 2.1(c)). For a query: H ow does sea w ater travel through the plant, and how does it change? this ontology m ay be used to reason as follows: A liquid MC from the sea is p u m ped into the boiler, w here it boils to form a steam MC. The steam MC is fed to the superheater and heated leading to a tem perature rise of the MC. Finally, the steam MC is supplied to the engine of the ship. 18 2.1.4 Limitations of Existing O ntologies The device ontology and the contained-liquid ontology are useful in reasoning about the dynam ic behavior of physical system s, and the piece-of-stuff is useful in reasoning about the equilibrium behavior of physical systems. H ow ever, they are inappropriate for reasoning about particulate system s w hich requires deeper understanding of causal m echanism s of constituent particles. C onsider the N aval Propulsion plan and a query: G iven the tem perature of the w ater from the sea increases, w hy is m ore steam generated in the boiler? A desirable answ er w ould be: Some of the liquid particles in the boiler possess kinetic energy enough to conquer the forces of attraction. Steam generation is the es cape of such high kinetic energy liquid particles from the surface into the surrounding atm osphere. The increased tem perature of the sea w ater m eans an increase in the num ber of such high kinetic energy particles, therefore, m ore steam is generated. This answ er involves the properties of constituent particles such as kinetic energy of liquid particles w hich is difficult to capture in the existing ontologies. For exam ple, suppose each particle is m odeled as a device w ith a property kinetic energy. Since the physical system is com posed of a large num ber of particles, reasoning becom es com putationally expensive. Even if w e succeed in reasoning about the individual particles in the particulate system , the obtained behavior is not useful since the behavior of the individual particles is transitory and random . The piece-of-stuff ontology assum es a uniform distribution of the properties of M C's. For the above query, because of this assum ption, this ontology w ould m odel the particles of the sea w ater in the boiler by one MC. H ow ever, the increase of steam generation can be explained only if a distinction betw een high and low kinetic energy particles is m ade. Hence, this ontology is not useful for m odeling such particulate systems. 19 Soil [[Oil L I * 8 6 .Solution Solution (a) (b) (c) Figure 2.2: Exam ple queries on a particulate system , a contained solution of w ater and salt. 2.2 M odeling Particulate Systems In general, the m odeling of a physical system should adhere to tw o basic princi ples: • Relevance principle: O nly objects and their properties that are relevant for reasoning purposes should be m odeled. • Parsimony principle: The m odel should include sufficient detail to reason about the posed query, and avoid extraneous materials. Consider the following three situations and their queries (Figure 2.2): • Q uery 1 W hat happens to the solution if the solution flows out from the container? (Figure 2.2(a)) • Q uery 2 W hat happens to the solution if w ater flows into the solution? (Figure 2.2(b)) • Q uery 3 W hy does the tem perature drop w ith evaporation? (Figure 2.2(c)) To answ er these queries, w e m ay construct m odels as depicted in Figure 2.3. 2 0 (^Sotation(wate^sait5) Solution (^Solution(watei^2t^) (^Sorverit(water)^) Soliuion Solute(salt) Solution( water,salt) Solvent(water) Solute(salt) Solution lowKE-particles) hiKE-particles Figure 2.3: M odeling contained solution for various queries. 1. The answ er to Q uery 1 is: the am ount of the solution decreases. To analyze this case, w e can m odel the solution w ith one object, a contained solution, w hich has properties such as the am ount of the solution (Figure 2.3(a)). W ith this m odel, w e can explain the decrease in the am ount of the solution. 2. The answ er to Q uery 2 is: the am ount of w ater in the solution increases, w hich leads to an increase in the am ount of solution and a decrease in the concentration. The previous m odel is insufficient to determ ine the concentration change. Therefore, w e need to m odel the solution w ith three objects, contained solution, contained w ater, and contained salt w ith properties such as concentration and am ount. Solution is com posed of w ater and salt. Hence w e can construct relations such that the am ount of 2 1 the solution is the sum of the am ounts of w ater and salt, the concentration of the solution is proportional to the am ount of salt, b u t inversely proportional to the am ount of water. W ith this m odel, w e can explain the increase in the am ount and the decrease in the concentration of the solution. 3. The answ er to Q uery 3 is: w ater particles escape into surrounding atm o sphere, resulting in decreases in the am ount and the tem perature of the solutions and an increase in the concentration. M odels for previous situ ations are not sufficient to explain the tem perature drop since a detailed m odel that distinguishes the escaping particles from non-escaping particles is required. Therefore, objects such as contained solution, contained water, contained salt, high kinetic energy w ater particles, and low kinetic energy w ater particles, are required. For these objects, w e can generate relations such that the am ount of the solution is the sum of the am ounts of w ater and salt, the concentration of the solution is proportional to the am ount of salt, and inversely proportional to the am ount of w ater, the tem perature of the solution is proportional to the tem peratures of w ater and salt, and the tem perature of the w ater is proportional to the population of high kinetic energy w ater particles, b u t inversely proportional to the population of low kinetic energy particles. W ith this m odel, w e can explain the tem perature drop, the am ount decrease, and the concentration increase. As is evident from the above exam ples, the sam e physical system m ay be m odeled at different levels of details and w ith different objects and their pro p erties depending on the posed queries. 2.2.1 Population-centered M odeling For particulate system s such as contained solution, it is not possible to m odel all the constituent particles since there are too m any of them , and it is not useful to m odel the solution as one object since sim ulation w ith the single object fails to provide explanations for queries such as Q uery 3. H ow ever, an im portant 2 2 observation is that a particulate system is com posed of a few collections of particles that behave distinctively — particles w ith high kinetic energy m ay escape from the pool of liquid particles, b u t particles w ith low kinetic energy cannot escape. Therefore, m odeling should focus on the collections of particles that provide qualitatively distinct behaviors. We call each such collection an aggregate and these aggregates form the basic objects for reasoning. A sim ple analysis of the exam ple show s that, for reasoning about the queries, the properties of the aggregate that w e consider are populations (e.g. the num ber of particles in the aggregate) and average values (e.g. average kinetic energy). Reasoning proceeds by determ ining the influences of interactions on populations of particle aggregates. The changes to the populations, in turn, affect the average values of quantities (e.g. a decrease in the population of high kinetic energy particle aggregate leads to a drop in the average kinetic energy of liquid particles). Since reasoning about changes to population of particle aggregates is cen tral to the changes of particulate system s, w e call our approach to m odeling population-centered modeling. In the population-centered m odeling, the populations m ay be hierarchical since one population m ay be com posed of several qualitatively distinct sub populations. Because of the hierarchical nature, there exist relations betw een the populations, w hich are used to propagate a change in a population to w hole particulate system s. These relations include: 1. Part-whole relations are the relations that hold betw een a population an d its parent population such as relations betw een w a te r/sa lt particle populations and solution particle population (Figure 2.4(b)) and betw een h ig h /lo w kinetic energy particle populations and w ater particle po p u la tion (Figure 2.4(c)). The population of the w hole is the sum of populations of the p arts (e.g. the population of the solution is the sum of populations of w ater and salt), and a property of the w hole depends on properties of the parts (e.g. the average kinetic energy of w ater particles depends upon the population of high kinetic energy particles). 23 (a) Solmion (^ S olu tion -partid e^ (b) u Solution Solution-partide^ (^ ^ ter-p artid es) (^Sali-particles) (c) Solution Solution-particle Water-particles Salt-partides) (^hiKE-particles^) (^w K E -partides) Figure 2.4: The population-centered m odels for contained solution for various queries. 2. Part-part relations are the relations that are true betw een tw o p arts such as relations betw een salt and w ater particles (Figure 2.4(b)) and betw een high and low kinetic energy particles (Figure 2.4(c)). For exam ple, random m otion of particles cause kinetic energies to be distributed over high and low kinetic energy particles in a regular form such th at they m aintain the shape of M axw ell's distribution[28j. This distribution shape constitutes p art-p art relations betw een high and low kinetic energy particles. These relations are used to propagate a change in a population to the w hole particulate system s. A decrease in a population of high kinetic energy particles, for exam ple, leads to the decreases in the am ount and average kinetic energy of 24 w ater particles, w hich in tu rn decrease the am ount of w ater in the solution and the tem perature of the solution. 2.2.2 The PA/AI O ntology U sing the population-centered m odeling paradigm , w e have developed a m od eling prim itive, particle aggregate (or sim ply PA) w hich represents population of qualitatively identical particles. M oreover, there exist processes w hich cause changes (such as escape, chem ical reaction, electrolysis, etc.) to the particle ag gregates. To m odel such processes, w e use a prim itive, aggregate interaction (or sim ply AI). The particle aggregates and aggregate interactions are described as follows: • A PA (Particle Aggregate) is a collection of particles that share com m on properties. A particle w ithin a particle aggregate m ay exist anyw here in the particle aggregate, that is, the location of a particle w ithin a particle aggregate is unim portant. • A n A I (Aggregate Interaction) is an interaction involving particle aggregates. W ith particle aggregates and aggregate interactions, w e can form relevant and parsim onious m odels of particulate system s w hich explicate deeper causal m echanism of constituent particles and overcom e the problem s of m odeling p ar ticulate system s. A m odel m ay be constructed w ith a few particle aggregates and aggregate interactions. The particle aggregates in the m odel are fine-grained enough for reasoning purposes and capture all the relevant know ledge of con stituent particles. The aggregate interactions in the m odel are not irregular or transitory in behaviors, b u t capture all the relevant know ledge for reasoning about the interactions. For instance, for Q uery 3, w e can construct the m odel w ith particle aggregates such as particle aggregates for solution particles, for w ater particles, for high kinetic energy w ater particles, for low kinetic energy w ater particles, and for 25 escaping Sol'iiion water-p (b) pop(water-p) = pop(highKE-p) + pop(IoKE-p) averageKE(water-p) qprop+ pop(highKE-P) averageKE(water-p) qprop- pop(IoKE-p) pop(solution-p) = pop(water-p) + pop(salt-p) averageKE(solution-p) qprop+ averageKE(water-p) etc. Figure 2.5: (a) A P A /A I m odel for particle escape in a particulate system (the ovals represent particle aggregates). Here, the particle aggregate of w ater p arti cles are divided into particle aggregates of high an d low kinetic energy particles, (b) The part-w hole relations th at hold betw een the particle aggregates. gas particles and one aggregate interaction for particle escape(Figure 2.5(a)). The part-w hole and p art-part relations that hold betw een the particle aggregates are show n in Figure 2.5(b). Using these particle aggregates and an aggregate interaction, a sim ulation algorithm m ay be able to infer that the high kinetic energy w ater particles escape, w hich results in the decreases in the population and the average kinetic energy of rem aining w ater particles. A ccording to queries, a particulate system m ay be m odeled differently since an interaction m eaningful to one query m ay not be so for another. The PA /A I ontology is flexible enough to focus on a m eaningful collection of particles and their interactions. C onsider the physical system of the solution of salt an d w ater in Figure 2.6. If a query involves the ionization of salt, the salt m ay be m odeled as three different particle aggregates: (1) salt m olecules, (2) sodium ions (N a+), and (3) chloride ions (Cl~). The NaCl m olecule of PAi dissociates to produce N a+ ions of PA2 and Cl~ ions of PA3, and the N a+ ions of PA2 and Cl- ions of PA3 interact to produce a NaCl molecule. H ow ever, if a query about evaporation is 26 vapor-p escaping Ionization/interaction, sodiujii-ion water-p PA, Solution ol salt PA2 p a 3 (a) (b) Figure 2.6: Different m odels for the sam e particulate system , (a) A m odel for a query about ionization, (b) A m odel for a query about evaporation. asked, the system m ay be m odeled w ith one particle aggregate for salt, for the dissociation of the salt into such ions is not im portant. 2.3 D iscussion The choice of ontological prim itives depends upon the queries posed for a given physical system . The device ontology is useful in sensitivity analysis, the contained-liquid ontology is useful in analyzing the dynam ic behavior of therm odynam ic or hydraulic system s, and the piece-of-stuff ontology is useful in reasoning about the changes to a contained fluid in equilibrium . The P A /A I ontology is useful in explicating the deeper causal m echanism s of particles con stituting particulate systems. The strengths of the PA /A I ontology include: (1) a focus on relevant collec tions of particles and their interactions, (2) not considering irregular individual behaviors of particles, (3) finding regular behavioral patterns over aggregates, and (4) flexible m odeling for different queries and ignoring non-relevant in teractions. H ow ever, this ontology has lim itations. Since the ontology neglects geom etries of individual particles or aggregates, it is difficult to analyze physical phenom ena such as Brownian m otion, random w alks of fluid particles, diffusion 27 of dye, chem ical bond structures, periodic properties, T hom pson's effect, and so on. These lim itations suggest directions for future research. In this chapter, w e discuss w hy existing ontologies are not useful for m odel ing particulate system s and describe the P A /A I ontology. The P A /A I ontology is useful because relevant and parsim onious m odels of particulate system s can be constructed using this ontology, and the analysis w ith these m odels expli cates deeper causal m echanism s based upon the constituent particles. In the next chapter, w e will describe the representation language for these ontological prim itives. 2 8 Chapter 3 Representation of Particle Aggregates and Aggregate Interactions The qualitative sim ulator takes, as input, a system m odel and a dom ain m odel. The system m odel is an ideal abstraction of a physical system relevant to the analysis of queries. The dom ain m odel includes general know ledge of the dom ain that is needed to analyze the system m odel. In this chapter, w e describe the qualitative representation of the system and dom ain m odels for qualitative analysis of particulate system s. 3.1 PS/IP Network A dom ain m odel contains theories for a dom ain at various levels of granular ity and perspectives. C onsider a sim ple physical system of a solution of salt dissolved in water. The dom ain m odel includes theories of various interactions such as fluid-flow, heat-transfer, dissolving, precipitation, condensation, evapo ration, ionization, chem ical reaction, and so on (Figure 3.1). H ow ever, according to the query about the physical system , w e m ay be interested in only a p a rt of the theories. If w e do not focus on that part, sim ulation becom es com plex, expensive an d w asteful. In m odeling a particulate system , w e superim pose a PS/IP network over m od els of the particulate system to select m odel segm ents relevant to the queries. 29 Solution of water and salt heat-transfer fluid-flow chlorine-ion dissoving s ionization _ r e a c tio u jfsodium-ion precipitation ^(Ttydrogen-ioj) ionization reaction ^^“ /oxygen-ion solution water water-flow escape capture Figure 3.1: For a sim ple physical system of solution w ith salt dissolved in water, the dom ain m odel m ay include theories on various interactions. A P S /IP netw ork is a netw ork of particle system s (PS) connected by interaction paths (IP) across w hich interactions m ay occur. Particle system s and interaction paths are defined as follows: • A particle system (PS) is a collection of particle aggregates (PAs) in w hich no relevant interaction occurs betw een the particles w ithin a system . • A n interaction path (IP) is a p ath connecting particle system s or environ m ents along w hich interactions take place. C onsider the exam ple of the salt solution and tw o queries regarding ioniza tion and evaporation (Figure 3.2). The physical system is the solution, and the dom ain m odel consists of m odels for particle aggregates such as salt particles, w ater particles, vapor particles, sodium ions, and chloride ions, and aggregate interactions such as ionization and evaporation. For the query on ionization, w e construct a P S /IP netw ork so that the salt is m odeled by three particle system s for sodium ions, chlorine ions, and salt particles, since there are interactions betw een these particle aggregates (Figure 3.2(a)). For the query on evaporation, w e build a PS /IP netw ork so that the salt is m odeled by one particle system w ith salt particles since there are no interactions of interest betw een the ions and betw een salt and w ater particles (Figure 3.2(b)). 30 salt-p V» Domain Models IP fo r escape IP f o r Ionization/interaction salt-p water-p chlorine-ion) ( sodium-ion Solution of water and salt Figure 3.2: P S /IP netw orks for the exam ples in Figure 2.6. By superim posing the netw ork over the particulate system , w e can choose m odels for the physical system that are relevant to the given query. 3.2 Representing Particle Aggregates and Aggregate Interactions In the previous section, w e described the P S /IP netw ork that is used for selecting appropriate m odel segm ents. In this section, w e describe the representation language for the P A / AI prim itives. 3.2.1 Preliminaries A m odel consists of objects, their properties, relationships betw een the proper ties, and interactions that change the objects and their properties. To represent objects and interactions, w e have developed P A /A I m odeling prim itives. To represent the properties of objects and their relationships, w e borrow som e con cepts used in Forbus' QP theory (Qualitative Process Theory) [15]. We briefly review these concepts: 1. Quantities are continuous param eters w hich are associated w ith objects, and are used to describe their properties (e.g. tem perature or am ount of a liquid). In QP theory, quantities are represented in term s of inequality 31 relations in the form of quantity spaces. N um bers are not used. A quantity has tw o parts, an amount and a derivative. A m ount represents the value of the quantity, and derivative represents the direction of change of the quantity. They can be negative, zero or positive. If a quantity has a positive am ount and a positive derivative, it has a positive, increasing value. 2. Qualitative Proportionalities describe the functional dependencies betw een tw o quantities qualitatively. Qprop+(Qi, Qz) represents the strict increas ing dependence of Q\ on Qz, and Qprop—(Qi, Qz) denotes strict decreasing dependence of Q\ on Qz- For instance, to represent that the acceleration (a) of an object is proportional to the force (f) exerted on it, w e use (Qprop+[a, f])- 3. Influences specify the direct effects of an active interaction (or process) instance. They are represented as [I±(Q, n)] based u p o n w hich, depending on w hether the num ber n has a positive or negative contribution to the derivative of Q, the sign of the derivative of Q is determ ined. For exam ple, the velocity (v) of an object is directly influenced by its acceleration (a), that is, (/+ [v , a]). Accordingly, the velocity is increasing, decreasing, or steady depending on w hether the net acceleration on the object is positive, negative, or zero. 3.2.2 Particle Aggregates A particle aggregate is a population of particles that share com m on properties. Particle aggregates m ay be hierarchical, hence there m ay exist p art-p art and part- w hole relations. In addition, particle aggregates can be created an d destroyed, and their properties can change dynam ically based upon active interactions. For exam ple, in the case of particle escape, a particle aggregate for liquid m ay disappear. O n the other hand, a particle aggregate for gas m ay be created w hile escape is active. These changes depend on the populations of the corresponding 32 particle aggregates. To represent such particle aggregates, w e need the follow ing pieces of inform ation: 1. PS: To describe a particle aggregate, w e m ust have a description of the particle system to w hich the particle aggregate belongs. This provides m odel selection preconditions. 2. Properties and Quantities: A collection of particles is characterized by the shared properties of the constituent particles. The properties of these parti cles are either nom inal properties (simply, properties) or continuous valued properties (simply, quantities). Q uantities are defined as described in QP theory. Properties and quantities are used to define different populations of particles. The distinction betw een properties and quantities is im por tant, for classification of particles according to nom inal properties, such as substance or phase of particles, is perform ed by the hu m an m odeler. H ow ever, classification according to quantities cannot be m ade in advance, since there can be a large num ber of classifications. Relevant classifications can be m ade w hen w e have inform ation on active interactions. For exam ple, w hen particle escape is considered, particles in a liquid particle aggregate m ust be classified at the barrier energy, not at any irrelevant values. That specific value cannot be located until w e know th at particle escape is active for the given physical system 1. 3. Conditions: PS, Properties and Quantities describe the preconditions for a particle aggregate to be instantiated. O n the other hand, to m odel dynam ic creation and destruction of particle aggregates during sim ulation, w e need conditions that m ake the instance active (created) and inactive (destroyed). Conditions state the conditions for the particle aggregate instance to be active. O ne of the obvious conditions for an active particle aggregate is that the num ber of constituent particles be greater than zero. 1We automate the process of classification according to landmarks, using a method called Interaction-Driven Particle Classification (IDPC). This process is described in Section 4.1. 33 4. Aggregate-Relationships: This segm ent describes the relationships betw een different particle aggregates. For representing these relations, w e introduce tw o novel quantities, population and average-quantity. Population denotes the num ber of particles in a particle aggregate, and average-quantity de notes the average value of a quantity for all the particles in the particle aggregate. Table 3.1(a) show s m odels of three particle aggregates, one for liquid parti cles, another for high kinetic energy liquid particles, and the third for low kinetic energy liquid particles. Each m odel is associated w ith a particle system , p ro p erties (e.g. substance and phase), quantities (e.g. kinetic energy), and aggregate relations betw een the particle aggregates. The m odel of the particle aggregate for liquid particles includes part-w hole relations. The population of liquid par ticles is the sum of tw o populations of high and low kinetic energy particles, and the average kinetic energy of liquid particles is proportional to the population of high kinetic energy liquid particles (since the m ore high kinetic energy p ar ticles exist, the higher the average kinetic energy of the w hole liquid particles becom es)2. Table 3.1(b) show s a P S /IP netw ork. In this netw ork, there are tw o p ar ticle system s, one for liquid particles and the other for gas particles, and one interaction p ath for particle escape that connects the tw o particle system s. 3.2.3 Aggregate Interactions A ggregate Interactions (AI) such as escape, capture and chem ical reaction, act th ro u g h tim e to cause changes to particulate system s. To represent aggregate interactions w e need the following pieces of information: 2We automated the processes of generating relations for the particle aggregates divided by IDPC. This process is described in Section 4.2. 34 Table 3.1: (a) Three particle aggregate m odel, (b) Scenario description of con tained water, (c) Its particle aggregate instances. ;; A model for particle aggregate of liquid particles ParticleAggregate (PA p-avr) PS: (ps ps-water) property: (substance water) (phase liquid) quantity: (ke (zero infinity)) conditions: (greater-than (pop (PA p-avr)) zero) aggregate-relationships: (Q= (pop (PA p-avr)) (+ (pop (PA p-hiKE)) (pop (PA p-lowKE)))) (qprop+ (ke (PA p-avr)) (pop (PA p-hiKE))) (qprop- (ke (PA p-avr)) (pop (PA p-lowKE))) ;; A model for particle aggregate of high KE liquid particles ParticleAggregate (PA p-hiKE) PS: (ps ps-water) property: (substance water) (phase liquid) quantity: (ke ((be water) infinity)) conditions: (greater-than (pop (PA p-hiKE)) zero) ;; A model for particle aggregate of low KE liquid particles ParticleAggregate (PA p-lowKE) PS: (ps ps-water) property: (substance water) (phase liquid) quantity: (ke (zero (be water))) conditions: (greater-than (pop (PA p-lowKE)) zero) ;; PS/IP network (ps ps-water) (ps ps-gas) (ip ip-escape ps-water ps-gas) (permit-phase-transition ip-escape) 35 1. IP: To describe an aggregate interaction, w e m ust have a description of the interaction path along w hich the aggregate interaction can occur. This provides m odel selection preconditions. 2. Individuals: The objects, either environm ental objects3 or particle aggre gates, that are required for an interaction to be applied. Particle aggregates m ay include descriptions of property and quantity values. 3. Conditions: IP, Individuals, Property, and Quantity descriptions describe the preconditions for instantiating an aggregate interaction. Individuals include particle aggregates, so for an aggregate interaction instance to be active, participating particle aggregates m ust be active. For particle escape, for exam ple, to be active, the population of liquid particles m ust be greater than zero. This segm ent describes the activity conditions for the aggregate interaction instance. 4. Aggregate-Relationships: A set of aggregate relationships are im posed by active interactions. To describe these relationships, w e introduce tw o ad ditional quantities, frequency and extent. Frequency represents the num ber of interaction instances of an aggregate interaction, an d extent represents the num ber of particle sites w here an interaction can occur. These quan tities m ay be influenced by other aggregate properties such as population and average quantity. The frequency of an interaction escape, for exam ple, depends both on the population of a particle aggregate for high kinetic energy particles and on the extent of the interaction (that is, the particles on the area of the surface of liquid w here escape occurs). 5. Influences: A set of influences on individual particles and on particle ag gregates by active interactions; the form er are represented by delete/add lists, and the latter are represented by [I±(Q,n)]. Delete-list states the 3For example, for an interaction, gaseous diffusion, to be active, a porous wall is required. 36 Table 3.2: A m odel for aggregate interaction escape. ;; A model for an aggregate interaction 'escape' Aggregatelnteraction (escape ?pa Pip) IP: (IP Pip Pps Pps2) (permit-phase-transition Pip) individuals: Ppa (PA Pps Psubs liquid (KE ((BE Psub) infinity))) conditions: (active Ppa) aggregate-relationships: exists a quantity (frequency Pself) (greater-than (frequency Pself) zero) (qprop frequency (extent Pip)) (qprop frequency (population Ppa)) delete-lists: disappears a particle of Ppa add-lists: appears a particle of Ppa-gas Ppa-gas (PA Pps-gas Psubs gas (KE (zero infinity))) aggregate-influences: (I- (population Ppa) frequency) (1+ (population Ppa-gas) frequency) p ro p erty /q u an tity descriptions of particles that do not hold after the in teraction occurs as well as disappearing particles. A dd-list states the new properties and quantities of particles th at hold after the interaction occurs as w ell as new ly generated particles. [I±(Q, n)] states the corresponding influences on particle aggregates. The definition of particle escape is show n in Table 3.2. For a particle escape to occur, a liquid particle and an interaction p a th w hich perm its phase transition are required. In addition, the particle should have kinetic energy greater than the barrier energy. If the particle escapes, due to phase transition, it becom es a gas particle. This is represented by the deletion of the liquid particle and the addition of the gas particle. Accordingly, the population of liquid particles decreases, an d the population of gas particles increases. The frequency of escape depends u p o n tw o factors, the extent of the interaction p ath and the population of high kinetic energy particles. 37 3.3 D iscussion The developm ent of the representations w as inspired by both STRIPS[38] and QP theory[15]. Like STRIPS, w e use add-lists and delete-lists in the representation of aggregate interaction to reflect the old and new facts of individual interacting particles. Like QP theory, w e use influences to describe the aggregate changes. P S /IP helps h u m an m odelers to select appropriate m odel segm ents. Recent w ork in autom ating the m odel selection process includes com positional m odel ing by Forbus and Falkenheiner[13]. They suggest a w ay to organize dom ain m odels and provide an algorithm to autom atically select the appropriate m odel segm ent by analyzing queries. In this chapter, w e describe the representation of particle aggregates and ag gregate interactions. To perform sim ulation, w e need inform ation on the types of particle aggregates that m ay exist in the particulate system u n d er investigation. In the next chapter, w e describe how to find such particle aggregates. 38 Chapter 4 PA Identification M ethod In real physical system s, particles are created and destroyed as tim e progresses. In sim ulation, the creation and destruction of the particles are im itated by ac tivities of corresponding particle aggregate instances. To perform sim ulation, these particle aggregate instances m ust be identified and available in advance. These particle aggregate instances include initially available types of particles, new ly created types of particles (e.g. particles such as the products of a chem i cal reaction), and classified particles (e.g. high kinetic energy particles an d low kinetic energy particles w hen escape is involved). W hen new particle instances are identified, relations for the new ly identified particles m ust be determ ined. The first step in qualitative sim ulation of particulate system s using the P A / AI ontology is to find all the physically realizable particle aggregate instances an d their corresponding relations. The PAI (Particle A ggregate Identification) m ethod finds particle aggregate instances that are relevant for reasoning p u r pose. It takes, as input, a set of particle aggregates initially available in the given physical system and applies potentially active interactions on them to identify new ly generated particles. W hile doing so, the PAI m ethod applies IDPC (Interaction-D riven Particle Classification) to classify particles in a p arti cle aggregate according to quantities as necessary. W hen IDPC is applied, new particle aggregates are generated for each of the classified particles, and new relations are generated for the particle aggregates. In this chapter, w e exam ine 39 IDPC and relation generation, then describe steps of the PAI process as w ell as how IDPC and relation generation are perform ed during these steps. 4.1 Interaction-Driven Particle Classification In C hapter 2, w e stated that ideal m odels of physical system s should be parsi m onious and relevant to the posed query, and that the P A /A I ontology serves as a m eans to construct such ideal m odels for particulate system s. In the ideal m odel form ed w ith the P A / AI ontology, different particle aggregates will behave differently and the particles w ithin a particle aggregate are treated identically. W henever particles in a particle aggregate show different behaviors, the particle aggregate m u st be divided to differentiate the particles. L andm arks [24] are values of quantities at w hich interactions becom e active or inactive such as freezing point or boiling point, and different behaviors of particles are caused by participations in active interactions. Accordingly, w hen an existing particle aggregate fails to provide the necessary fine-grained division to differentiate particles participating in an interaction from those that do not, the particle aggregate m ust be divided at the landm ark of the interaction. This division process is called interaction-driven particle classification (IDPC). Consider the contained-w ater exam ple of Figure 4.1. In the sim plest case, all the w ater particles m ay be treated as identical, and the entire collection m ay be m odeled by a single particle aggregate. In this case, continuous-valued properties of the particles such as kinetic energy w ill be represented by an interval (0, oo). H ow ever, if reasoning involves interactions such as escape, the particle aggregate m odel m ust be sufficiently fine-grained to distinguish betw een the particles that participate in the interaction, those w ith kinetic energy greater th an barrier-energy, (BE, oo), and those that do not, those w ith kinetic energy less than barrier-energy, (0, BE). In this case, the m odel of the contained w ater m ust include tw o particle aggregates as show n in the figure. 40 Figure 4.1: Particle classification of the contained-w ater exam ple: the particles in a container is initially m odeled by a single PA (1). W hen w e consider the interaction escape w e classify particles in it to form tw o particle aggregates according to their kinetic energy (2 and 3). 4.2 Generating Relations C onsider the contained-w ater exam ple involving escape. W hen a liquid particle aggregate is divided into high and low kinetic energy particle aggregates by IDPC, new causal relations should be introduced to determ ine the qualitative behavior of the system. These relations include: (1) part-whole relations (e.g. the population of liquid particles is the sum of populations of h igh an d low kinetic energy particles, and the average kinetic energy is qualitatively proportional to the population of high kinetic energy particles, since the m ore high kinetic energy particles exist, the higher average kinetic energy of liquid particles becom es.), (2) part-part relations (e.g. relations betw een high and low kinetic energy particles d ue to kinetic energy redistributions.), and (3) part-interaction relations (e.g. the interaction escape has direct influence on high kinetic energy particle aggregate.). 4.2.1 Characteristics of Interactions These relations are generated in accordance w ith the characteristics of the in teractions that play a role on particle classification. We w ill exam ine these IDPC part-w hole relations E g. Q+[pop(liq-PA), pop(loKE-PA) part-interaction relation E.g. I-[pop(hiKE-PA), freq(Escape)] p a rt-p a rt relations E.g. KE redistributions Figure 4.2: W hen an interaction particle escape is potentially active in liquid particles, IDPC classifies the particles in the liquid particle aggregate to form high and low kinetic energy particle aggregates. For these new ly generated particle aggregates, som e relations are im posed, such as part-w hole, part-p art and part-interaction relations. characteristics, then describe how the relations are generated according to these characteristics. We define the follow ing characteristics of interactions: 1. Upper and lower thresholding interactions: As in particle escape, an interac tion m ay occur only to particles w ith a quantity value greater (or less) than a threshold value. We call this quantity thresholdingh A particle aggregate is divided to distinguish interacting from non-interacting particles b y IDPC only w h en such quantity thresholding is in effect. W hen an interacting particle has a quantity value greater than a threshold, w e call it an upper- thresholding interaction on the corresponding particle aggregate. W hen an interacting particle has a quantity value less than a threshold, w e call it a lower-thresholding interaction on the particle aggregate. 2. Entering and exiting interactions: A n interaction m ay increase or decrease the population of a particle aggregate. W hen an interaction increases the 1 We borrowed the concept of thresholding from [3]. 42 population of a particle aggregate, w e call it entering interaction to the particle aggregate, and w hen an interaction decreases the population of a particle aggregate, w e call it exiting interaction from the particle aggregate. 3. Active and passive interactions: The population of a particle aggregate m ay or m ay not have influence u p o n the frequency of an aggregate interaction. If it influences the frequency of an aggregate interaction, the interaction is called active in the particle aggregate. The interaction is called passive in the particle aggregate, otherw ise. For illustration, w e exam ine the three interactions given in Figure 4.3. Con sider the first interaction, escape (Figure 4.3(a)). Particle escape occurs only to the liquid particles w hose kinetic energy is greater than barrier energy. W hen its phase transits to gas, the kinetic energy is not thresholded at the gas particles.2 The m ore high kinetic energy particles exist, the m ore particles escape. There fore, escape is an interaction w hich is upper-thresholding on liquid particles, b u t not thresholding on gas particles; exiting from high kinetic energy liquid particles an d entering to gas particles; and active in high kinetic energy liquid particles, yet passive in gas particles. Consider the second interaction, capture (Figure 4.3(b)). Particle capture occurs to any gas particle if the gas particle hits the surface of collection of liquid particles, during random m otion in the atm osphere. The m ore gas particles exist, the m ore gas particles are captured. Therefore, capture involves no thresholding on both gas and liquid particles, hence no classification or relations are m ade. We can characterize it as an interaction w hich is exiting from gas particles and entering to liquid particles; and active in gas particles, an d passive in liquid particles. Consider the last exam ple, vaporization (Fig ure 4.3(c)). W ater gas particles in the air, if they cool dow n sufficiently or hit vapors surrounding them , transit phase from gas to w ater, w hich in tu rn form s a collection of vapors. This process is called vaporization an d is used to explain 2During the phase transition, the energy corresponding to the barrier energy is consumed, hence resulting level is not thresholded. 43 Vaporization Capture hiKE-Iicf PA . vapor PA upper-thresholding no thresholding no thresholding no thresholding low-thresholding no thresholding exiting-from entering-to entering-to exiting-from exiting-from entering-to active-in passive-in passive-in active-in active-in active-in Figure 4.3: Three exam ples that illustrate characteristics of interactions: (a) escape, (b) capture and (c) vaporization. how clouds an d rains are form ed. The m ore gas particles exist, the m ore gas p a r ticles cool dow n, and the m ore vapor particles exist, the m ore gas particles m ay hit vapor particles. Vaporization is an interaction w hich is lower-thresholding on gas particles, b u t no thresholding on vapor particles; exiting from gas particles and entering to vapor particles; and active in both gas and vapor particles. 4.2.2 Types of Relations The u p p e r and low er thresholding interactions trigger IDPC to divide a particle aggregate into tw o particle aggregates. W hen the particle aggregate is divided, new relations m ust be form ed to reflect the changes in the m odel. These relations are sum m arized in Table 4.1. The table involves five types (Type A to E) of qualitative relationships for the divided particle aggregates. These relations are of part-w hole and part-interaction relations.3 They involve quantities such as frequencies (FREQ,), average-quantities (AVR(Q,P)), populations for divided particles that are influenced b y an interaction I; (POP,(P)), and represented by relationships such as qualitative proportionalities (Q prop±) and influences (I±). The characteristics of interactions are expressed in x„ y, and z, in the table. W hether tw o different interactions (T and I?) influence the sam e particles or not is reflected in k A l l of x„ y„ z, and k ,j are used to determ ine the directions 3Part-part relations due to kinetic energy redistributions are discussed in the next chapter. 44 Table 4.1: Types of relations for classified particles. Given: P = A particle aggregate. Q = A quantity of P. I = A set of interactions (Ii, I2/ ..., In) that may become active for P ac cording to the value of Q. Each I; is either an upper-thresholding or a loiver-thresholding interac tion with a threshold (TH,), either an entering or an exiting interac tion, and either an active or passive in a certain PA. POP(P) = The population of P. AVR(Q, P) = The average-quantity of P for Q. FREQ, = The frequency of an interaction, I;. POP,(P) = A partial population of P which participates in I,. Relationships: Type A Type B Type C Type D Type E where, POP(P) qprop POPi(P) AVR(Q, P) qprop x, * POP,(P) POP,(P) FREQ, FREQ, (i = 1,... , n) (i = 1,... , n) (i = 1,... , n) qprop z, * POP,(P) (i = 1,... , n) qprop z, * kitj * POPj(P) (j = 1,... , n; i = 1, I y, * FREQ, x ,: = y; z = [+] if I; is an upper-thresholding interaction, [-] if I,- is a lozver-thresholding interaction. [+] if I,- is an entering interaction to POP,(P), [-] if I, is an exiting interaction from POP,(P). [+] if I,- is active in POP,(P), [0] if I,- is passive in POP,(P). [+] if POP,(P) fl POP^P) ± 0. [0] if POP,(P) n POPj(P) = 0. of the changes in the qualitative relationships. These relations are described as follows: • Type A describes part-w hole relations on populations, w hich are the quali tative proportionality from the population of a divided particle aggregate (POP,(P)) to that of the particle aggregate to w hich the divided particle aggregate belongs (POP(P)). The direction of the change is alw ays positive, hence (qprop+ POP(P), POP,(P)) 45 is established for all interactions, from Ii to In. Type A relations include that the population of liquid particles is qualita tively proportional to the populations of high and low kinetic energy liquid particles. • Type B describes part-w hole relations on average quantities, w hich are the qualitative proportionalities from a population of a divided particle aggre gate (POP;(P)) to an average quantity of a particle aggregate to w hich the di vided particle aggregate belongs (AVR(Q,P)). If I, is an upper-thresholding interaction (i.e. X ; = [+]), the particles in POP;(P) have the quantity Q greater than TH;, hence the larger POP;(.P) is, the greater average quantity of Q for the w hole particles becom es. Therefore, (qprop+ AVR(Q,P), POPt(P)) is established. Similarly, if I; is a low er-thresholding interaction (i.e. X ; = H)/ (q p ro p - AVR(Q,P), POP;(P)) is established. Such relations are established for all interactions, from Ii to I n - Type B relations include that the average kinetic energy of liquid particles is qualitatively proportional to the population of high kinetic energy particles. • Type C describes part-interaction relations regarding direct influences, w hich are the direct influences of an interaction (FREQ;) on the population of a di vided particle aggregate (POP;(P)). If I; is an entering interaction to POP;(P) (i.e. y; = [+]), (1+ POP;(P), FREQ;) is established. Similarly, if it is an exiting interaction from POP;(P) (i.e. y; = H)/ 46 (I-PO Pi(P), FREQ,) is established. Such relations are established for all interactions, from Ii to In- Type C relations include that the active interaction escape results in a decrease in the population of high kinetic energy liquid particles, and an increase in the population of gas particles. • Type D describes part-interaction relations regarding frequencies, w hich are the qualitative proportionalities from a population of a divided p arti cle aggregate (POP,(P)) to the frequency of the corresponding interaction (FREQ;). If I; is active in POP,(P) (i.e. z, = [+]), (qprop+ FREQ;, POP;(P)) is established. If it is passive in POP;(P) (i.e. z, = [0]), relation is not established. Type D relations include that the frequency of escape is qualitatively pro portional to the population of high kinetic energy particles. • Type E describes part-interaction relations upon frequencies, w hich are the qualitative proportionalities from a population of a divided particle aggre gate (POPj(P)) to the frequency of different interactions (FREQ;). POP;(P) is the population of a particle aggregate w hich is divided b y I;, and POPj (P) is the population of a particle aggregate w hich is divided b y I,. For POPj (P) to have influence u p o n FREQ;, I; m ust be active in POP,(P) (i.e. z, = [+]) and POP;(P) and POPj(P) m ust overlap (POP;(P) n POPj(P) f 0, i.e. k,u = [+])• If so, (qprop+ FREQ;, PO P^P)) is established. O therw ise, no relation is established. Suppose w e p o u r hot w ater w hose kinetic energy is greater than som e value above zero, into a contained water. Then escaping frequency increases. 47 Type E relation, captures the required relation for this situation. T hat is, the frequency of escape qualitatively proportional to the population of the hot water. C onsider an exam ple of contained w ater w hich involves tw o interactions, particle escape and freeze (Figure 4.4). Freeze occurs w hen a liquid particle w ith very little kinetic energy hits the surface of the ice in the w ater an d transits its phase from liquid to solid. For the interactions in this exam ple, tw o thresh old values of kinetic energy exist, one for escape and the other for freeze. We call them BE-escape and BE-freeze, respectively. IDPC is applied to distinguish betw een escaping and non-escaping, and freezing and non-freezing particles. Consequently, IDPC w ill divide the liquid particle aggregate (PA;;?) into four divided particle aggregates, a particle aggregate for particles w ith kinetic en ergy low er th an BE-escape (PA;e), a particle aggregate for particles w ith kinetic energy greater than BE-escape (PA^e), a particle aggregate for particles w ith ki netic energy low er than BE-freeze (PA;/), and a particle aggregate for particles w ith kinetic energy greater than BE-freeze (PAhf)- For these particle aggregates, relations are generated and added to the m odels of corresponding particle ag gregates and aggregate interactions. Such relations are described in Figure 4.4. The relations in (a) are part-w hole relations on populations (Type A) from the divided particle aggregates (PA he, PA;e, PA hf, and PA;/) to the liquid particle ag gregate (PA/jg); the relations in (b) are part-w hole relations on average quantity (Type B) from the divided particle aggregates to the liquid particle aggregate; the relations in (c) are part-interaction relations on direct influences (Type C) from escape and freeze to PA/ie and PA;/; the relations in (d) are part-interaction relations on frequencies from a divided particle aggregate to the frequency of an interaction w hich is used to divide the particle aggregate (Type D). T hat is, from PA he to escape and from PA;/ to freeze; and the relations in (e) are part- interaction relations upon frequencies from a divided particle aggregate to the frequency of an interaction w hich is independent from dividing the particle ag gregate (Type E). That is, from PA hf to escape and from PA;e to freeze. This 48 w aiei PA for lowKE-e KE = (0, BE-escape) \ KE PA for highKE-e PA f°r lowKE-f PA for highKE-f KE = (BE-escape, °°) KE = (0, BE-freeze) KE = (BE-freeze, » ) / 0 BE-escape 0 BE-freeze Let: FAavr PA,e PA he PAf/ PA,/ PA gas A PA of liquid particles with kinetic energy between zero and oo. A PA of liquid particles with kinetic energy between zero and BE-escape. A PA of liquid particles with kinetic energy between BE-escape and oo. A PA of liquid particles with kinetic energy between zero and BE-freeze. A PA of liquid particles with kinetic energy between BE-freeze and oo. A PA of gas particles. Relations: (a) Type A - part-whole relations on populations. (QPROP+ (Population PAatir) (Population PA;e)) (QPROP+ (Population PAa ilJ .) (Population PA,e)) (QPROP+ (Population PA0 i ,jr) (Population PA;/)) (QPROP+ (Population PAavr) (Population PA,/)) (b) Type B - part-whole relations on average quantities. (QPROP+ (KE PA0„r) (Population PA,e)) (QPROP- (KE PAaur) (Population PA;e)) (QPROP+ (KE PAai,r) (Population PA,/)) (QPROP- (KE PAa t,r) (Population PA;/)) (c) Type C - part-interaction relations on influences. For FREEZE. Since ice is not a particle aggregate, influences upon ice is not shown. (I- (Population PA,e) (Frequency ESCAPE)) (1+ (Population PA5a5) (Frequency ESCAPE)) (I- (PopulationPA;/) (Frequency FREEZE)) (d) Type D - part-interaction relations on frequencies. (QPROP+ (Frequency ESCAPE) (Population PA,e)) (QPROP+ (Frequency FREEZE) (Population PA;/)) (e) Type E - part-interaction relations on other frequencies. These relations are generated only if (BE-Freeze > BE-Escape). (QPROP+ (Frequency ESCAPE) (Population PA;/)) (QPROP+ (Frequency FREEZE) (Population PA, e)) Figure 4.4: For the exam ple of contained w ater involving escape and freeze, IDPC divides the w ater particle aggregate into four particle aggregates. For these particle aggregates, relations are generated and added to the m odel instances of particle aggregates and aggregate interactions accordingly. 49 type of relations will be generated only w hen tw o classified particles overlap (i.e. BE-freeze > BE-escape); otherw ise, they are not generated. 4.3 The PAI M ethod Interactions can create new particles and destroy existing particles in physical system s. Hence the set of particles that exist at a certain point of tim e m ay be different from the set of particles in the initial situation. The PAI (Particle A ggregate Identification) m ethod com putes the tim e evolution of the initial set of particles by generating a state transition diagram . The state transition diagram (called a particle-state interaction-transition diagram or P-I diagram) is com posed of a collection of states in w hich a set of particles exists (called a particle-state or p-state) an d transitions w hich lead from a p-state to another b y active interactions (called an interaction-transition or i-trans). The state transition diagram tells all the particles that m ay exist in the system at any point of tim e an d how they are created. The PAI m ethod takes initial p-state then applies potentially active interac tions on it to find new p-states. It repeats this process until no new p-states are introduced to the p-i diagram . W hile doing so, the PAI m ethod applies IDPC. Table 4.2 sum m arizes tw o m ain algorithm s for the PAI m ethod and IDPC. The detailed steps of the PAI m ethod are as follows: 1. Determining potentially active interactions. The interaction m odels of the dom ain are first exam ined to check if their preconditions are satisfied by any collection of particle aggregates in the current p-state. The preconditions of an interaction include the individuals and IP. The interactions w hose preconditions are satisfied are considered to be potentially active interactions and collectively constitute an i-trans. 2. Applying IDPC and relation generation to the current p-state. 50 Table 4.2: Two algorithm s for the PAI m ethod and IDPC. Data Structures: Sg: Q ueue of p-states to be explored. Sc: Current p-state being explored. Ps: Set of PAs in state S. I m: M odels of interactions. Ic: Set of active interactions for Sc. Q Cic: Inequalities in quantity-conditions of Ic. R ic: Inequalities in results of Ic. Inequalities: QCic or R jc. Q: A quantity in an Inequalities. Im: A landm ark compared w ith Q in Inequalities. Ss: Set of successor p-states that result from applying Ic to Sc. Algorithm the PAI method: Si = initial p-state; S'* - {S i}; Until (Sg = empty) do Sc = pop(5?); I c = determine-active-interactions(5,c/ Jm); Sc = apply-IDPC-and-generate-relations(<QC7c, Sc); Ss = genera te-successor-p-states(S'c, Ic) Ss = apply-IDPC-and-generate-relations(/^/c, Ss); For each of state S' in Ss do Connect i-trans (Ic) from state Sc to S; Sq = pushnew(,S’, Sq); End for; End until; Algorithm HyPC(Inequalities, Sc): Q = the quantity of a particle in Inequalities; Im = the landm ark that is compared w ith Q in Inequalities; Ps = the set of PAs in S c; Find a PA from Ps whose interval, (h , h)r overlaps w ith Im, that is, l\ < lm < h) If found, Set the PA to Poverlapr Split Poverlap into tWO PAs, by partitioning the interval, (l\, 1 2), into ( h ,lm) and (lm, I2); End if; 51 The next step is to apply, if necessary, IDPC to the particle aggregate to distinguish interacting and non-interacting particles based on the quantity of the particle aggregate described by the potentially active interactions. The classification is perform ed by partitioning the relevant quantity in terval of the selected particle aggregate. That is, if one of the current particle aggregates has an interval that overlaps the interval described in the quantity description of a potentially active interaction, the particles in the particle aggregate is classified to form tw o different particle aggre gates. W hen IDPC divides particle aggregates, relations are generated for the divided particle aggregates according to the characteristics of the active interactions. 3. Generating the successor p-states. By applying the active interactions to the current p-state, the successor p-states are generated. In dealing w ith a new ly generated particle, if the current p-state already has a particle, the successor state need not introduce it again. H ow ever, if the particle does not exist in the current p-state, it is introduced to the successor states. In dealing w ith a disappearing particle, tw o possibilities are asserted: (1) the disappearing particle is the last particle in the current state, or (2) there is m ore than one particle represented by the disappearing particle. We consider both of these cases for generating successor states. 4. Applying IDPC and relation generation to successor states. This step applies IDPC to the particle aggregates in the successor p-states to distinguish the particle aggregates resulting from the active interactions. T hat is, if the successor p-state includes a particle aggregate, and it has quantity interval that does not m atch that of current particle aggregates, the particle aggregate in the successor state is divided. W hen IDPC di vides particle aggregates, relations are generated for the divided particle aggregates accordingly. 52 escape [p2 -> p4] [p\= (PS-a, 1 , (0, particle-classification p2 = (PS-a, p3 = (PS-a, 1 , (0, be)) J / ST-1 p2 = (PS-a, 1, (be, ooj) p3 = (PS-a, 1, (0, be)) P4 = (PS-v, g, (0, oo)) escape [p2 -> p4] Water P4 = (PS-v, g, (0, ~ )) Figure 4.5: The P-I diagram generated for the contained-w ater exam ple. In this figure, pn is a particle aggregate, PS-a and PS-v are particle system s for contained-w ater and vapors, I and g m ean the phases of pn's, nam ely liquid and gas, and (11,12) is the interval for kinetic energy. 5. Connecting transitions between current and successor states. I-trans established in step 1, is connected from the current p-state to all the successor p-states and added to the P-I diagram . Finally, each of the successor p-states is exam ined to check if any of the states in P-I diagram has the sam e set of particle aggregates. The p-states that do not have sam e sets are inserted into the queue for next iteration of this procedure. C onsider the situation involving the evaporation of the contained-w ater (Fig ure 4.5) — assum e that, initially, there is no w ater vapor above the surface of contained water. Suppose, initially, the h u m an m odeler m odeled one particle aggregate for the w ater liquid (pi). Since there is no vapor particle, only one particle aggregate exists in the initial state (ST-0). The first step finds that the in teraction escape is active. To distinguish escaping from non-escaping particles, the second step classifies particles in the PA (p i) to form tw o particle aggregates w hich have kinetic energy greater and less than barrier-energy w hich are p2 and p3, respectively, then generates relations for these divided particle aggregates. 53 The third step finds all the possible successor states because of the active inter action escape. In this case, the successor states include the state in w hich the liquid particle still rem ains (ST-1), and the state in w hich no m ore liquid particles are left (ST-2).4 H ow ever, both states contain vapor particles w hich appear due to the active interaction escape. The fourth step classifies the particles in the particle aggregates in the successor states (ST-1 and ST-2). Yet, in this case, since the new ly appearing gas particle has the sam e kinetic energy level as the one in the current state (ST-0), no classifications or relations are m ade. The final step augm ents the P-I diagram by adding i-trans of escape from the current p-state, ST-0, to the successor p-states, ST-1 and ST-2. This w hole process is repeated until all the p-states and i-trans are found. 4.4 D iscussion In this chapter, w e describe the PAI m ethod w hich finds qualitatively im portant particle aggregate instances required for qualitative sim ulation of particulate system s. Interestingly, the PAI m ethod can be used to generate explanations of particle's behavior. Consider the contained-w ater exam ple show n in Figure 4.5. Suppose w e are interested in a description of evaporation in term s of the particles constituting the contained water. From the generated the P-I diagram , w e can generate a description such as: "A m ong the liquid particles in the container, som e have sufficient high kinetic energy to conquer the inter-m olecular attractive forces. The particles w ith high kinetic energy m ay escape into the surrounding atm osphere, thereby changing from a liquid particle to a gas particle." Similarly, the P-I diagram can answ er som e exam ple queries given in Section 1.5 such as appearance of hydrogen gas (Example 3). 4According to the distribution of kinetic energies of liquid molecules [28], as far as there exist liquid particles, some of them have kinetic energy enough for escape. Hence, no escaping particle implies no remaining particle. Therefore, in this diagram, we assume that all the low kinetic energy particles disappear when all the high kinetic energy particles disappear. 54 IDPC described in this chapter classifies particles in a particle aggregate to form tw o particle aggregates by a single threshold value and generates rela tions accordingly. It is possible to divide a particle aggregate into m ore than tw o particle aggregates. H ow ever, w e find that it is difficult and expensive to generate relations, especially for average-quantities and frequencies (Type B, D and E). N onetheless, there is no extra gains of inform ation useful for sim ulation w ith the m ultiple classification com paring w ith our m ethod. The reason is the qualitativeness of the calculus used in the qualitative sim ulation. We can think of tw o cases in w hich such m ore-than-tw o classifications are m ade: (1) Classification by multiple thresholding (e.g. an interaction occurs to the particles that have a quantity value betw een tw o intervening threshold values); (2) Classification by multiple interactions (e.g. w hen m ore than one thresholding interactions occurs w ith different threshold values). The first case is rare in practice for the natural or artificial physical system s that w e are interested in. The second case is not rare, b u t w e need inform ation on the relative m agnitude of tw o involved threshold values. If the inform ation is not available, w e need to m ake assum ptions on the relative m agnitudes for all the possible cases, w hich will produce a proliferation of relations. Even though such assum ptions are m ade, resulting part-w hole relations are not useful in com puting the properties such as average quantities. In the next chapter, w e describe the m odeling of particle aggregates, aggregate interactions, and other pieces of inform ation useful for qualitative sim ulations, then illustrate actual sim ulation of several selected examples. 55 Chapter 5 M odeling and Sim ulation W hen all the qualitatively im portant particles have been identified, the next step is to select a sim ulator and perform sim ulation w ith the particle m odels. For the sim ulator, w e use QPE (Qualitative Process Engine) [17], an im plem entation of Q P theory[15]. For the qualitative analysis of particulate system s, w e need additional know ledge such as kinetic energy redistribution an d interconnecting theories to perform sim ulation. In this chapter, w e briefly introduce QP theory and describe how to represent, in Q P language, our m odels of particle aggregates, aggregate interactions, ki netic energy redistributions, and interconnecting theories. A t the end, w e show several sim ulation exam ples. 5.1 QP Theory In Q P theory, the physical objects in the system are m odeled as views, an d the things that cause changes in the physical system s are m odeled as processes. Both processes and view s can change dynam ically as sim ulation proceeds. In quali tative analysis of particulate system s, particle aggregates are the physical objects and aggregate interactions are the causes of the changes. Particle aggregates and aggregate interactions are also dynam ic and involve changes on continuous aggregate properties. We use QPE to perform sim ulation on particulate system s. 56 H ence w e use views and processes to m odel particle aggregates and aggregate interactions, respectively. We will briefly review the views and processes of QP theory and the reasoning m ethod of QPE. 1. View (or Individual-View) is used to represent dynam ic objects. A n Individual- View has four pieces of inform ation: individuals, preconditions, quantity- conditions, and relations. Individuals and preconditions describe the con ditions for a view instance to exist. Q uantity conditions describe the con ditions for the view instance to be active. Relations specify the causal relations that hold as a consequence of an active view instance. 2. Processes are represented in a m anner sim ilar to the individual-view . In ad dition to the four com ponents, it has an extra com ponent, influences, w hich describes the direct causal influences, [I±(Q, n)], of the active process in stance. 3. Reasoning Method: QPE takes, as input, a description of the physical sys tem s and the qualitative dom ain m odel. QPE com putes the qualitative behavior (called envisionment) of a physical system in four steps: (1) it de term ines w hich individual-view instances and process instances exist and m ay becom e active, (2) it determ ines all the consistent states by varying activities of individual-view and process instances, (3) for each state, it determ ines changes in the quantities due to active process instances, (4) fi nally, it determ ines all possible transitions am ong the states. A t the end, the envisionm ent, a description of the behavior, is available. 5.2 M odeling PA/AI In this section, w e describe how w e represent particle aggregates and aggregate interactions using individual-view s and processes. 57 5.2.1 Particle Aggregates Table 5.1(a) illustrates the definitions of particle-aggregates for therm odynam ic system s. In therm odynam ic system s, particles are characterized by substance, phase, and kinetic energy level. In addition, for sim ulation, additional inform a tion on a particle system to w hich a particle aggregate belongs is needed. These are described in individuals of view definition. The PAI m ethod identifies all the im portant particle aggregates. The scenario description for QPE sim ulation includes these particle aggregates (Table 5.1(b)). U sing preconditions, the view instances are generated for the particle aggregates. For these view instances to be active, the population should be greater than zero, w hich is described in quantity conditions. Finally, relations of view definitions describes the facts that are true w h en the view instance is active. H ow ever, in this definition, no specific relationships are given. For the exam ple of a contained-liquid involving escape, the PAI m ethod identifies four qualitatively im portant particle aggregates: liquid particles, high and low kinetic energy liquid particles and gas particles. The descriptions of these particle aggregates are given in the scenario description to satisfy the preconditions of the view definition (Table 5.1(b)). For these particle aggregates, QPE generates corresponding view instances (Table 5.1(c)). The first aggregate instance represents the liquid particles, the second represents the liquid particles w ith low kinetic energy, the third represents the liquid particles w ith high kinetic energy, an d the last represents the gas particles. W hen IDPC classifies the particles, it generates relations that are true betw een the particle aggregates such as part-w hole relations, i.e. the population of liquid is proportional to the populations of the high kinetic-energy particles, and the average kinetic energy of liquid particles is proportional to the population of the high kinetic-energy particles. These relations are show n in Table 5.1(d). 58 Table 5.1: (a) The individual view definition for the particle-aggregates in ther m odynam ic particulate system s, (b) The scenario description for particle aggre gates identified by the PAI m ethod, (c) Particle aggregate instances generated, (d) A ggregate relationships betw een the particle aggregates. (a) ;; QPE representation of particle aggregates for thermodynamic ;; systems. {defview (part-aggr (PA ?ps ?subs ?ph ?int)) individuals ((?ps :type ps) (?subs :type substance) (?ph :type phase) (Pint :type ke-interval)) preconditions ((form-a-PA ?ps Psubs Pph Pint)) quantityconditions ((greater-than (A (pop (PA Pps Psubs Pph Pint))) zero)) relations (((v-i (PA Pps Psubs Pph Pint)) Pself))) (b) ;; Particle aggregates identified by the PAI method. (form-a-PA ps-water water liquid (ke (zero infinity))) (form-a-PA ps-water water liquid (ke (zero (be water)))) (form-a-PA ps-water water liquid (ke ((be water) infinity))) (form-a-PA ps-gas water gas (ke (zero infinity))) (c) ;; Three particle aggregate instances. (PA PS-WATER WATER LIQUID (KE (ZERO INFINITY))) (PA PS-WATER WATER LIQUID (KE (ZERO (BE WATER)))) (PA PS-WATER WATER LIQUID (KE ((BE WATER) INFINITY))) (PA PS-GAS WATER GAS (KE (ZERO INFINITY))) (d) ;; Their aggregate relationships (QPROP (POP (PA PS-WATER WATER LIQUID (KE (ZERO INFINITY)))) (POP (PA PS-WATER WATER LIQUID (KE ((BE WATER) INFINITY))))) (QPROP (KE (PA PS-WATER WATER LIQUID (KE (ZERO INFINITY)))) (POP (PA PS-WATER WATER LIQUID (KE ((BE WATER) INFINITY))))) 59 Table 5.2: A process definition fo r the interaction escape. (defProcess (escape ?pa-liq ?pa-gas ?ip) individuals ((?pa-liq :type (PA ?ps-liq ?sub liquid (K E ( (BE ?sub) infinity)))) (?pa-gas :type (PA ?ps-gas ?sub gas ?int-gas)) (?ip :type (IP ?ip ?ps-liq ?ps-gas))) preconditions ((permit-phase-transition ?ip ?ps-liq ?ps-gas)) quantityconditions ((active ?pa-liq) (greater-than (A (extent ?ip)) zero)) relations (((p-i (escape ?pa-liq ?pa-gas ?ip)) ?self) (quantity frequency) (greater-than (a frequency) zero) (qprop+ frequency (extent ?ip)) (qprop+ frequency (pop ?pa-liq))) influences ((I- (pop ?pa-liq) (A frequency)) (1+ (pop ?pa-gas) (A frequency)))) 5.2.2 Aggregate Interactions Table 5.2 show s the representation for the aggregate interaction escape. For an instance of the interaction escape to exist, there m ust be particle aggregates for high kinetic energy liquid particles and gas particles and an interaction p a th w hich perm its phase transition. For the interaction instance to be active, the population of the high kinetic energy particles m ust be positive, an d the extent of the interaction p ath m ust be positive. W hen the interaction instance is active, the interaction is associated w ith a quantity frequency w hich represents the n u m b er of escaping particles. The frequency of interaction escape is influenced by the extent of the interaction p ath and the population of the high kinetic energy particles. The influence p art describes the direct influences of the interaction. T hat is, the population of particle aggregate of high kinetic energy decreases, and the corresponding population w ill appear in the particle aggregate for the corresponding gas. 60 Escape pop pop pop KE BE pop KE Figure 5.1: A ccording to M axw ell's distribution, it is not physically possible that low kinetic energy particles rem ain w hen all the high kinetic energy particles escape into atm osphere. 5.3 M odeling Kinetic Energy Redistribution Since PA /A I m odeling of a particulate system ignores irregular m otions of p a r ticles, it fails to capture som e significant physical phenom ena. Fluid particles display random collisions. According to the distribution of kinetic energies of fluid particles[25], the random collisions of fluid particles result in a redistribu tion of kinetic energy over the particles. D ue to the redistribution, the particles m aintain a certain distribution of kinetic energy over population, w hich is called M axw ell's distribution. Consider the particle escape exam ple. W hen high ki netic energy liquid particles escape, random collisions cause som e low kinetic energy to obtain kinetic energy enough for escaping. Therefore, it is not p h y s ically realizable that any low kinetic energy particles rem ain w hen all the high kinetic energy particles escape into atm osphere (Figure 5.1). Two behavioral patterns of the redistributions in term s of particle aggregates are: (a) both p o p ulations of high and low kinetic energy particle aggregates are either zero or positive sim ultaneously and (b) w hile particle escape occurs, the population of low kinetic energy particle aggregate decreases, and the corresponding am ount increases in the population of high kinetic energy particle aggregate, w ith the rate less than evaporation rate until both populations reach zero at the sam e time. 61 Table 5.3: M odels of kinetic energy redistribution w hich includes (a) a m odel to m ake tw o particle aggregates of h igh and low kinetic energy coexist, an d (b) redistributory com pensation processes to keep them coexistent. (a) ;; Two PAs divided by kinetic energy always coexist, (defperspective (Redistributory-Relations ?loKEp PhiKEp ?avrKEp) individuals ((?loKEp :type (PA Pps ?sub Pph (KE (zero Pthresh)))) (PhiKEp :type (PA Pps Psub Pph (KE (Pthresh infinity)))) (PavrKEp :type (PA Pps Psub Pph (KE (zero infinity))))) relations ((correspondence ((a (population PloKEp)) zero) ((a (population PhiKEp)) zero)) (Q= (population PavrKEp) (+ (population PloKEp) (population PhiKEp))))) ( b ) interaction compensatmjr — Th Th Th Th upper-thresholding upper-thresholding lower-thresholding low er-thresholding exiting interaction entering interaction exiting interaction entering interaction ;; Redistributory compensation process to be used for upper- ;; thresholding exiting interaction such as 'particle escape'. (defprocess (Compensatory-Redistribution (?p-i PlowerPA PupperPA)) individuals ((PlowerPA :type (PA Pps Psub liq (?q (Plow-bound Pthresh)))) (PupperPA :type (PA Pps Psub liq (?q (Pthresh Pupper-bound)))) (?p-i :type (aggregate-interaction ?p-i) :conditions (upper-thresholding ?p-i PupperPA) (exiting-from ?p-i PupperPA))) quantityconditions ((active ?p-i)) relations ((quantity frequency) (greater-than (a frequency) zero) (less-than (a frequency) (a (frequency ?p-i)))) influences ((1+ (population PupperPA) (a frequency)) (I- (population PlowerPA) (a frequency)))) 6 2 To represent (a), w e use QPE prim itives such as defperspective and correspon dence: defperspective is used to im pose relationships that hold w hen som e p re conditions are m et, and correspondence is used to m ap value inform ation from one quantity to another[15]. Table 5.3(a) represents the facts w hen a particle aggregate is divided into tw o particle aggregates according to kinetic energy, if one of the divided particle aggregates has zero population, the other also has zero population and the population of liquid particle aggregate is the sum of the tw o populations. To represent (b), w e introduce redistributory compensation processes represented by a QP theory prim itive, process. As in part-w hole and part-interaction relation generation, these com pensatory processes are m ade according to the charac teristics of interactions. Characteristics of interactions such as u p p er or low er thresholding and entering or exiting determ ine the direction of com pensation betw een divided particle aggregates. Four types of com pensatory processes are constructed according to the types of interactions such as upper-thresholding exiting, upper-thresholding entering, low er-thresholding exiting, and lower- thresholding entering interactions. Table 5.3(b) depicts the types of com pen satory processes and includes a QPE representation for upper-thresholding ex iting interactions such as particle escape. In this representation, if an upper- thresholding exiting interaction is active, the population of u p p er divided p arti cle aggregate decreases. This m akes the com pensatory process becom e active to m ove particles from low er divided particle aggregate to u p p er divided particle aggregate at a frequency w hich is less than the interaction frequency. 5.4 M odeling Interconnecting Theories Interconnecting theories describe the relationships betw een the particle and contained-liquid ontologies, and are used to obtain the CL(contained-liquid)- level behavior from the com puted particle behavior. Since the particle behavior includes changes in existence and quantities of particle aggregates, the tw o 63 Table 5.4: The interconnecting theory corresponding to the entity contained- liquid. (defview (contained-stuff (C-S ?sub liquid ?can)} individuals ((?pa :type {PA ?ps ?sub liquid {KE (zero infinity)))) (?can :type container)) quantityconditions ((active ?pa)) relations (((v-i ?cs) ?self) ;; Interconnecting theories on amount and temperature (qprop (amount (C-S ?sub liquid ?can)) (population ?pa)) (correspondence ((a (amount (C-S ?sub liquid ?can))) zero) ((a (population ?pa)) zero)) (qprop (temperature (C-S ?sub liquid ?can)) (ke ?pa)) {correspondence ((a (temperature (C-S ?sub liquid ?can)) zero) ((a (ke ?pa)) zero)))) im portant relations are the existence relationships from particle aggregates to contained-stuffs and the causal relationships from the quantities of particle ag gregates to the quantities of the contained-stuffs. Table 5.4 show s an interconnecting theory required to generate the CL-level behavior for the contained-w ater exam ple involving escape. The interconnect ing theory specifies that a contained-liquid instance exists w h en a liquid particle aggregate instance exists, and the instance becom es active w h en the particle aggregate is active. W hen the contained-liquid instance is active, causal rela tions hold such that the am ount of the contained-liquid is proportional to the population of the liquid particles, and the tem perature of the contained-liquid is proportional to the average kinetic energy of the liquid particles. 64 5.5 Sim ulation Figure 5.2 show s an exam ple envisionm ent and the explanation for the tem per ature drop in the evaporation exam ple. For illustration, only one interaction escape is considered. The figure show s (1) the m odels for particle aggregates, aggregate interaction, com pensatory process, along w ith the interconnecting theory, (2) the structural description in term s of particle aggregates an d their various properties, (3) the resulting envisionm ent, and (4) the explanation for the tem perature drop. QPE com putes the behavior and generates the envision m ent for the given situation. From the envisionm ent, w e illustrate one state w here particle aggregates of high and low kinetic energy particles and inter actions of escape and com pensatory process are active. Interpretation of the selected state description im plies that though interactions escape and its com pensatory process are active, since the frequency of escape is greater th an the frequency of the com pensatory process, the population of high kinetic energy particles decreases. Then, the population and average kinetic energy for the liq uid particles decreases, resulting in decreases in the am ount and the tem perature of the contained-w ater. 5.6 A dditional Simulation Examples In this section, w e briefly describe tw o additional exam ples involving situations of the evaporation in a contained-solution and the chem ical reaction show n in Figure 1.4. For simplicity, com pensatory processes of kinetic energy redistribu tion have been left out of the figures. The first figure (Figure 5.3(a)) describes w h y the evaporation rate drops in the contained-solution. O ne state that corresponds to the figure is show n in detail. Interpretation of the state description reveals that a decrease in the high kinetic energy particles leads to a decrease in the population of the w ater particles. Since the concentration of salt becom es higher, m ore escaping sites on the surface of 65 defView (PA ?ps?phase ?ke-interval) defProcess (escape ?PA1 ?PA2 ?IP) defPerspective(Redist-Rel ?hiKEp ?loKEp) defProcess (Redist-Comp ?hiKEp ?loKEp) (qprop+ (temp contained-water) (KE (PA ?ps liquid (ke (0 « )))) (qprop+ (amount contained-water) (pop (PA ?ps liquid (ke (0 °°)))) Models QPE Envisionment v Description for one state /fa c tiv e PA-liquid) (active PA-highKE-liquid)) (active PA-lowKE-liquid)) (active PA-vapor) (active contained-water) (active (escape PA-highKE-liquid PA-vapor)) (> (freq escape) zero) (I- (pop PA-highKE-liquid) (freq escape)) (1+ (pop PA-vapor) (freq escape)) (qprop+ (pop PA-liquid) (pop PA-highKE-liquid)) (qprop+ (aver-KE PA-liquid) (pop PA-highKE-liquid)) (qprop+ (temp contained-water) (aver-KE PA-liquid)) (qprop+ (amount contained-water) (pop PA-liquid)) (dec (pop PA-liquid)) (dec (pop PA-highKE-liquid)) (dec (KE PA-liquid)) (dec (pop PA-highKE-liquid)) (dec (temp contained-water)) (dec (amount contained-water)) /^ P S PS-water) (PS PS-gas) (IP ip-escape PS-water PS-gas) (subs water) (phase liquid) (phase gas) (form-a-PA ps-water liquid (ke (0 =»)) (form-a-PA ps-water liquid (ke (be °°))) (form-a-PA ps-water liquid (ke (0 be))) (form-a-PA ps-gas gas (ke (0 < * > ))) Structural description Explanation for temperature drop escape is active ( Redist-comp is active freq(comp) > zero ftpop of hiKE particles Upop of lowKE V particles freq(escape) > zero I 1 ' It pop of hiKE particles Q+ [Q + ■ 1 1 aver kinetic energy l Q+ u pop of particles l Q + ■ I t temp of water U amnt of water Figure 5.2: A sim ulation exam ple for particle escape in the contained w ater (See Figure 1.3). A n explanation for the tem perature drop is given. 66 Description for one state Solution Explanation for evaporation-rate drop / ( a c t i v e PA-salt) (active PA-water)) (active PA-highKE-water)) (active PA-vapor) (active contained-solution) (active (escape PA-highKE-water PA-vapor) (> (freq escape) zero) (I- (pop PA-highKE-water) (freq escape)) (1+ (pop PA-vapor) (freq escape)) (qprop+ (pop PA-water) (pop PA-highKE-water)) (qprop+ (extent IP-escape) (pop PA-water)) (qprop+ (freq escape) (extent IP-escape)) (dec (pop PA-highKE-water)) (dec (pop PA-water)) (dec (extent IP-escape)) (dec (freq escape)) escape is active , * escape frequency > zero I'- ■ U pop of high-KE particles J,Q+ U pop of water particles J,Q+ U extent of IP J,Q+ 1 1 escape frequency \ (b) n . \io ri \oci Description for one state active PA-NO) (active PA-C12)) (active (chem-reaction NO Cl2 NOC1 Cl)) (qprop-t- (speed PA-NO) (KE PA-NO)) (qprop+ (speed PA-C12) (KE PA-C12)) (qprop+ (extend IP-chem-reaction) (speed PA-NO)) (qprop+ (extend IP-chem-reaction) (speed PA-C12)) (qprop+ (freq chem-reaction) (extent IP-chem-reaction)) (inc (KE PA-NO)) (inc (KE PA-C12)) (inc (speed PA-NO)) (inc (speed PA-C12)) (inc (extent chem-reaction)) V (inc (frequency chem-reaction)) Explanation for chem-reaction-rate rise heating is active If aver KE of reactants 1 1 pop of high-KE reactants | 1 1 aver speed of reactants Q + I Q + y 11 1 extent of chem-reaction • N . 1 1 chem-reaction frequency Figure 5.3: Two additional sim ulation exam ples, (a) Evaporation rate drop in solution (Figure 1.4(a)), and (b) the reaction rate increase due to heating (Figure 1.4(b)). 67 the w ater are taken by salt particles, im plying the decrease in the extent of the IP. Therefore, the frequency of escape decreases, since the frequency is dependent on the extent of the IP. The second figure (Figure 5.3(b)) show s how the reaction rate increases due to heating. The heating of the container results in an increase in the kinetic energy for both reacting particles, N O and CI2. The increase in the kinetic energy raises the speed of the particles, in tu rn increasing the collision frequency betw een reacting particles. Since the sites of the chem ical reaction are form ed w hen tw o reacting particles collide, the increased collision frequency im plies the increased extent of the IP for chem ical reaction. A t the sam e tim e, the populations of high kinetic energy reacting particles increase by heating. Both of the increases in the extent and the populations of high kinetic energy reacting particles contribute to the increase in the chem ical reaction rate. 5.7 D iscussion In this chapter, w e describe how to represent, in QP language, m odels of p ar ticle aggregates, aggregate interactions, kinetic energy redistributory process, and interconnecting theories and illustrate several sim ulation exam ples from therm odynam ic system s and chem istry using QPE. R edistribution com pensation m odels m ake u p a type of p art-p art relations for particle aggregates that are divided according to kinetic energy. It is different from other part-w hole and part-interaction relations (Type A through Type E) in tw o aspects: (1) Redistribution com pensation is hard to m odel using sim ple qualitative relations w ithout introducing processes, since it requires m odeling of changes in populations of IDPC-classified particle aggregates due to random m otion; (2) T hough other types of relations are generally applicable to classified particles by any quantity, redistribution com pensation is restricted to a specific quantity, kinetic energy, since the com pensation is m odeled after M axw ell's kinetic energy distribution model. 68 It m ay be possible that no p art-p art relations are required as in solute and solvent particles in a solution. O n the other hand, the parts m ay exchange p o p ulations in a regular pattern. If liquid particles are classified according to kinetic energy, they m aintain the populations to preserve the M axw ell's distribution shape. If liquid particles are classified by constituent particles' m oving direction such as u p w ard , dow nw ard, and sidew ard-m oving particles, they keep the fixed ratio betw een the populations. If liquid particles in a container are classified by the exposure to the air, the population of the exposed particles depends u p o n the shape of the container. If the patterns are regular and system atic, w e m ay be able to m odel them using com pensatory processes as done in kinetic energy redistribution. 69 Chapter 6 Related Work In this chapter, w e discuss previous w ork on ontologies, particulate system s, m ultiple m odels, and aggregation. 6.1 O ntologies O ntological selection is the process of determ ining how to m odel the com ponents an d their properties so that they are relevant to the analysis of the physical system . In this section, w e review w idely used ontologies for reasoning about physical system s and their lim itations for reasoning about particulate system s. • In the device ontology[9,10], a physical system is com posed of devices. A device is described by a set of param eters, a set of causal relations betw een param eters that are im posed by the device, and a set of I /O ports. A physical system is m odeled as a netw ork of devices. • In the contained-liquid ontology[15, 13, 17], a physical system consisting of fluids is m odeled as fluids in containers w ith properties due to con tainm ent. Interactions resulting in changes to the properties of fluids are m odeled by processes. 70 • In the piece-of-stuff ontology[7, 20], a system is m odeled as a collection of pieces, called m olecular collections (MC), and reasoning involves deter m ining the p ath of the piece through the physical system and the changes to it at each com ponent on the path. Reasoning about the m olecular collection is typically perform ed based on the results of reasoning at the contained- liquid ontology [15]. • In the plug-flow ontology[41], a system is m odeled as a fluid p a th an d a plug of fluid flowing through the path. This ontology is developed for reasoning about spatially distributed behaviors of fluid flow. The plug- flow ontological prim itive is used to reason about the detailed changes to the properties, such as tem perature and phase, of the p lu g at different spatial locations w hile flowing through a path. The contained-liquid and the device ontology are inappropriate for reasoning about particulate system s. For exam ple, suppose each particle is m odeled as a device. Since the physical system is com posed of a large n u m b er of particles, reasoning becom es com putationally expensive. Even if w e succeed in reasoning about the individual particles in the particulate system , the obtained behavior is not useful since the behavior of the individual particles is transitory and irregular. Both the piece-of-stuff ontology and plug-flow ontology assum e a uniform distribution of the properties of MC or plug. In the w ater evaporation exam ple of Figure 1.3, because of this assum ption, these ontologies w ould m odel the particles of the contained w ater by a single object. H ow ever, the tem perature drop in the w ater can be explained only if a distinction betw een high an d low kinetic energy w ater particles is m ade. Hence, these ontologies are n o t useful for m odeling such particulate systems. 71 6.2 Particulate Systems Recently, several researchers[35, 3,26] have addressed reasoning about particu late system s. In this section, w e review their w ork an d discuss their strengths and lim itations for reasoning about particulate system s. • Rajam oney and Koo[35] perform qualitative sim ulation about particulate system s at the particle level, of w hich results propagate to contained liquid level using interconnecting theories. • A m ador and Weld[3] perform qualitative sim ulation about particulate sys tem s by using three levels of m odeling: particle level, aggregate level and contained-liquid level. They perform sim ulation at the particle level and propagate the result to contained-liquid level behavior using statistical operators. • Liu and Farley[26] introduce the charge-carrier (CC) ontology for p ertu rb a tion analysis about electronic devices. Their em phasis is on the autom atic shift betw een the device ontology and the CC ontology, based on the anal ysis of given queries. In our previous work[35], w e provided prelim inary w ork for qualitative analysis of particulate system s. We perform ed sim ulation at the particle level an d propagated its result to aggregate level for com puting contained-liquid level behavior to explicate deeper m echanism s of particle behaviors. H ow ever, our initial w ork lacked sim ulation at aggregate levels, particle classification facilities, and m odels for kinetic energy redistributions. T hough A m ador and W eld's w ork is sim ilar in spirit, there are som e dif ferences. They perform sim ulation at the particle level, instead of aggregate level, and propagate the result using their statistical operators to determ ine the behavior of populations. They lack the particle classification facility w hich is im portant for decom posing particle aggregates as n eeded based on interactions. 72 As a result, to perform qualitative sim ulation, the hum an m odeler m u st be given all the types of qualitatively im portant particles in advance. Liu and Farley w orked on particulate system s. H ow ever, the particles in their w ork are restricted to charge carriers. T hat is, the applicable dom ain of their approach is lim ited to electronics, and reasoning is restricted to p erturbation analysis since the m ethod is not detailed enough to handle the existence changes of particles or charge carriers. 6.3 M ultiple M odels For m ost engineering and scientific tasks, typically no single m odel suffices. M ost physical system s are sufficiently com plex that a precise m odel is too ex pensive to m anipulate. A num ber of researchers have used m ultiple m odels or levels of abstraction in qualitative reasoning. • H ayes [20] initially proposed m ultiple ontologies for therm odynam ic sys tem s and claim ed that tw o ontologies exist for the liquid dom ain, contained- liquid and piece of a liquid, and neither of them suffices alone. This w ork m otivated the developm ent of the piece-of-stuff ontology[20] b y Forbus and Collins. • Collins and Gentner[6] analyzed the phenom ena of evaporation an d con densation through psychological studies and developed three m odels that people use at different levels of detail: m olecular m odels, aggregate m odels and m acroscopic models. • Liu and Farley[26] m aintain tw o theories for electronics, one based on the charge carrier ontology and the other based on the device ontology, and according to the query, control shifts betw een the tw o different theories. Several other researchers have investigated m ultiple ontologies in therm ody nam ic system s, such as [35], [6], [3], [26], [7] and [42]. In our research, w e focus 73 on the know ledge at the deeper level of the particles com prising the physical sys tem s, and perform sim ulation w ith the deeper theories to com pute m acroscopic behavior. 6.4 Aggregation O ur w o rk addresses qualitative reasoning about physical system s that are com posed of a large num ber of particles. Several researchers have w orked on aggre gation and abstraction to facilitate reasoning qualitatively about such com plex physical system s. • Liu and Farley[27] have show n how to use structural aggregation to sim plify com plex physical system s. They replace a collection of devices in a physical system by an equivalent aggregate. Then they autom ate the se lection of appropriate structural aggregates based on the given task. Their approach has been applied to pressurized hydraulic system s an d electronic circuits for the tasks of operation, diagnosis, and explanation. • Weld[42] has investigated behavioral aggregation in causal sim ulation in his PEPTIDE system. In his w ork, a repetitive cycle of processes is aggre gated into a continuous process description of the cycle's behavior. His system uses the history structure to recognize repeating cycles of processes and generate a higher-level abstraction of the system 's behavior. • R ouquette and Rajamoney[40] have investigated form ing behavioral ag gregates w ithin com plex system s, particularly, dynam ic aggregates — ag gregates w hose activity depends on operating conditions that vary over the sim ulation. In their w ork, an aggregate consists of a causal p attern w hich exhibits a regularity in behavior, such as regulation or equilibrium , that can be m odeled and reasoned about. They show how such causal p at terns m ay be detected in the causal netw ork of a com plex physical system , 74 and behavioral aggregates m ay be hypothesized u n d er assum ptions about operating conditions. • Rajam oney and Lee [34] has show n how to form an d use functional aggre gates w ithin a com plex physical system to sim plify its qualitative analysis. A functional aggregate is a particular configuration of devices that achieves a specific function. In structural aggregation, the aggregates are form ed w h en a particular con figurations of devices, such as serial or parallel layouts, are detected regardless of functionalities or behavioral regularities. In behavioral aggregation, the aggre gates are form ed w hen a cluster of devices show s a regular behavioral patterns, such as regulation and equilibrium . In functional aggregation, the aggregates are form ed w h en a configuration of devices show s a specific functionality. Structural aggregates are easiest to find in a physical system b u t least useful in reasoning. Functional aggregates are hardest to form b u t m ost useful, and behavioral ag gregates are in betw een. All the above aggregation m ethods start from detailed m odels to abstract m odels to sim plify qualitative analysis. O n the other hand, our w ork starts from abstract m odels to finer grained m odels — IDPC classifies particle aggregates w h en it is required for reasoning purposes. 6.5 D iscussion Recently, efforts w ere m ade to autom atically construct or select qualitative m od els of physical system s. [2], [13] and [29] propose w ays to autom atically select p ro p er m odel segm ents from a system atically organized m odel base, by analyz ing queries or expected behaviors of given physical system s. In [4], the NATSIM system builds qualitative m odels of system dynam ics through n atu ral language interface. In [39] and [36], qualitative m odels of a dom ain are constructed by analyzing the raw data of the given physical systems. The fram ew ork, proposed 75 in this thesis, perform s sim ulation w ith qualitative m odels of particle aggregates and aggregate interactions. W hile doing so, it constructs m odels as necessary. The PAI m ethod autom atically constructs m odels for divided particle aggregates and generates relations for the particle aggregates, based on available m odels of particle aggregates and reasoning requirem ents. The underlying principles of this m odel construction are the parsim ony and relevance principles w hich facilitate generation of ideal models. 76 Chapter 7 Evaluation In this thesis, w e have described our fram ew ork for the qualitative analysis of particulate system s. We evaluate our fram ew ork based on the coverage of pro b lems. First, w e take an in-depth look at a particular dom ain: chemistry. We exhaustively investigate exam ples from a college-level chem istry textbook, Col lege Chemistry by Bruce H. Mahan (1966)[28], to find out the coverage of exam ples by this fram ew ork, and im plem ent representative exam ples. Second, w e exam ine several particulate system exam ples from various dom ains such as biology, electronics, and economics. 7.1 The Chemistry Dom ain We investigate each exam ple in the selected chem istry textbook and classify them into tw o groups: particulate and non-particulate system s. Then w e classify the particulate system s into tw o classes: one class that our m ethod can handle and the other class that our m ethod cannot handle. We analyze the involved exam ples according to the order of the chapters in the textbook. Table 7.1 sum m arizes the results. 1. In the first three chapters, the properties of m atter in gas, liquid, and solid phases and the related exam ple experim ents are described. M atter in gas or liquid phase is naturally a particulate system , and its experim ents are 77 Table 7.1: The coverage of exam ple problem s in the chem istry dom ain. Exam ples are borrow ed from College Chemistry by Bruce H. Mahan (1966). book examples particulate Can extensions chapters shown systems? handle? required property ideal gas laws yes yes of gases gaseous diffusion yes yes property all the examples no — no particle's of solids motion liquids and phase transition yes yes solutions its equilibrium yes yes equilibria in solutions yes yes chemical chemical reaction yes yes equilibrium chemical equilibrium yes yes ionic ionization yes yes equilibria acids and bases yes yes weak and strong acids yes no OMR acid-base titrations yes no numerical info. multistage equilibria yes no relative strengths oxidation and galvanic cell yes yes reductions electrolysis yes yes chemical expansion force of gas yes yes thermodynamics heat and work yes yes thermochemistry yes yes chemical concentration effects yes yes kinetics temperature effects yes yes collision theory of gases yes yes catalysis yes yes electronic structure Thompson's experiment yes no geometric reasoning of atoms prism effects yes no geometric reasoning chemical bond bond structures no — individual particles periodic properties all the examples no — individual particles metallic elements all the examples no — individual particles non-metallic bond all the examples no — individual particles transition metals all the examples no — individual particles organic chemistry all the examples no — individual particles nucleus radioactive decays yes no aggregation 78 w ell suited for our m ethod. H ow ever, since the constituting objects of m atter in the solid phase are fixed in location and do not show transitory or irregular behaviors, they are not classified as particulate system s. We im plem ented exam ples involving phase transitions, phase equilibrium , tem perature effects to equilibrium , concentration effects to equilibrium in solutions, and gaseous diffusion. 2. In the next five chapters, various chemical reactions and related topics are described. These are also particulate system s and w e find that m ost of the exam ples can be handled by our m ethod. H ow ever, there are som e exam ples that cannot, including differentiating strong and w eak acids, m ultistage equilibria am ong w eak acids, and base and acid-base titra tion. In these chapters, w e im plem ented exam ples involving chem ical re action, ionization, oxidation, reduction, electrolysis, chem ical equilibrium , tem perature effects in chem ical equilibrium , and concentration effects in chem ical equilibrium . 3. In the next chapter, electronic structures of atom s are described. T hough the collections of atom s are particulate system s, exam ples such as Thom pson's experim ent and prism effects can not be handled by o u r m ethod since they require spatial (or geom etrical) reasoning. 4. In the subsequent six chapters, properties of individual m olecules and their various bond structures are described. Individual particles them selves are not particulate system s. 5. The last chapter is on the nucleus. Radioactive decay requires reasoning about behavioral aggregation of particle aggregates[33], w hich is not a part of this research. From the exam ples that can be handled by our m ethod, w e selected represen tative exam ples to perform m odeling and sim ulation. These results of m odeling and sim ulation for the selected exam ples are discussed below. 79 Phase Transitions Phase transitions occur to fluid particles b y particle escape and capture. Particle escape occurs w hen a liquid particle w ith kinetic energy greater th an barrier energy changes its phase from liquid to gas, a n d particle capture occurs w h en a gas particle changes its phase from gas to liquid. C onsider three scenarios show n in Figure 7.1(a). The first scenario is a con tained w ater in an open vessel; the second scenario is a contained w ater in an open vessel w hich is being heated; and the third scenario is a contained solution in an open vessel. For these scenarios, the PAI m ethod finds that interaction escape and cap ture are potentially active. H ence it classifies the liquid (and solvent) particles into tw o different particle aggregates, high and low kinetic energy particles, to distinguish escaping from non-escaping particles. The PAI m ethod also gener ates qualitative relationships for these classified particles and identifies the gas particle w hich can be generated by particle escape. These particle aggregates are show n in Figure 7.1(b). (In the figures of particle aggregates th roughout this chapter, solid ovals represent initially available particle aggregates, an d dotted ovals represent the new ly identified or classified particle aggregates by the PAI m ethod.) W ith m odels of these particle aggregates, qualitative sim ulation using QPE explains the queries in Figure 7.1(c): 1. W hy does the temperature drop? W hen high kinetic energy particles escape, the population of high kinetic energy particles decreases; therefore, the average kinetic energy for rem aining liquid particles also decreases. Since tem perature of the liquid is proportional to the average kinetic energy of liquid particles, the tem perature of the contained w ater drops. (Details of the program ru n on this problem are illustrated in A ppendix A.) 2. Equilibrium? W hen high kinetic energy particles escape, the population of rem aining high kinetic energy particles decreases and the population of 8 0 (a) Scenarios involving phase transitions. Wnicr Water (b) PAs identified by the PAI method for the scenarios. /fii-KE-p*; rio-KE--p ; gas-p • • ------ Solvent \ gas-p ) ^i-KE-ph flo-KE-pV * •------ ^ ' (c) Example queries and their explanations provided by qualitative simulation. “Whv temperature drops?” escape is active freq(escape) > zero V - ■Upop(hi-KE-p) n |,Q + -Uavr-KE(liq-p) \|/ Q+ ■Llterap(contained-liquid) “How to reach equilibrium?” When freq(escape) > freq(capture) escape is active freq(escape) > zero / i - 1 + ilpop(hi-KE-p) ftpop(gas-p) ^ Q+ Q+ ^ Jlfreq(escape) 1 T freq (capture) “Temperature effect?’’ heating is active llavr-I^k(liq-p) „ 4.Q + ftpop(hi-KE-p) ^Q+ ITfreq(escape) “Concentration effect?” escape is active „ ^ I+ Ipop(hi-KE-p) \j/Q+ llpop(solvent-p) \J/ Q+ ■U-extent(escape) 4^q+ lifreq(escape) Figure 7.1: (a) Situations involving phase transitions, (b) Q ualitatively im portant particle aggregates identified by the PAI m ethods, (c) Explanations for various queries. 81 gas particles increases in the corresponding am ount. Some of gas particles are captured into liquid particles. Since the frequency of escape depends u p o n the population of rem aining high kinetic energy liquid particles, and the frequency of capture depends upon the population of gas particles, the escaping frequency decreases, and capturing frequency increases until they reach an equilibrium state. 3. Temperature effect? W hile the contained w ater is being heated, the p o p ulation increase of high kinetic energy particles leads to the increase in the frequency of escape. 4. Concentration effect? As the solvent particles escape, m ore area of the surface of the solution is occupied by solute particles, an d that leads to a decrease in the escaping sites of the solvent particles. Therefore, the frequency of escape decreases. Chemical Reactions A ccording to chem ical kinetics, chem ical reaction occurs w h en tw o m olecules w ith sufficient kinetic energy collide and interact to produce new molecules[28]. C onsider three scenarios show n in Figure 7.2(a). The first scenario is a closed vessel w ith NO(g) and 0 2 (g), initially. The second scenario is a sam e vessel w hich is being heated. The third is the sam e scenario as the first one in w hich b o th forw ard and reverse reactions, NO(g) + 0 2 (g) - NOCl(g) + Cl(g), and NO(g) + 0 2 (g) - NOCl(g) + Cl(g), are considered. For these scenarios, the PAI m ethod finds that the forw ard chem ical reac tion is potentially active, thereby classifying the reacting m olecules, such as N O (g) and Cl2(g) according to the kinetic energy. This classification is done to 8 2 (a) Scenarios involving chemical reactions. Cl2 NO Cl NOCl Cl, \o Cl NOCl ©2 ^ Cl NOCl NO(g) + Cl2(g) -» NOCl(g) + Cl(g) NO(g) + Cl2(g) » NOCl(g) + Cl(g) (b) PAs identified by the PAI method for the scenarios. Sfif-KE-NO-p 'y /ht-K E-N O C i-p-> 'No-p'^^r---------- ^ * • ----------- % _ r N o c : i - p - /'hi-KE-NO-p'A ^NO-p^ri- " /SiocT-p) Cl2-p ?1b-KE-NO-p*; C fif-KE-CI^-p"', ^1o^K E -N O -p'^ ;rio-K E -N O C l-jff^ CliT-KE-Cf2 -p'*; ,^'hT-KE-Cl'p‘--> ClrP ^ L _ ^ --------------- ------------------- P >To-KE-Cl2:p > (c) Example queries and their explanations provided by qualitative simulation. --------- ^ C 1 .p^ ^-KE-Cia-p^ r.;to-KE-Cl-p*;5 ' “Whv Cl appears?” chemical reaction is active “How to reach equilibrium?” When freq(for- reaction) > freq(rev-reaction) freq(reaction) > zero ttpopjci-p) ‘Temperature effect?’- for-react is active V U-pop(hi-NO-p) freq(for-reaction) > zero 1 + \ + ffpop(Cl-p) heating is active I+ I + \ (NO Havr-KE(NO-p) fTavr-KE(Cl2-p) . 'i'Q+ 4zQ + irpop(hi-NO-p) frPop(hi-CI2-p) \ Q + / * Tlfreq(reaction) Q + 1 Upop(hi-Cl2-p) 1Tpop(NOCl2-p) J Q + . , v 'J' ^ + w ftpop(hi-Cl-p) lifrcq(for-reaction) ftpop(hl.NOCL-p), /Q+ Q + Itfreq(rev-reaction) Figure 7.2: (a) Situations involving chem ical reactions, (b) Q ualitatively im p o rtan t particle aggregates identified by the PAI m ethods, (c) Explanations for various queries. 83 distinguish reacting from non-reacting molecules. Then the PAI m ethod gener ates qualitative relationships for these new ly classified m olecules and identifies m olecules produced by chem ical reaction, such as NOCl(g) and Cl(g). (For the third scenario, since reverse interaction is also considered, NOCl(g) and Cl(g) are classified, too.) These particle aggregates are show n in Figure 7.2(b). W ith such m odels of particle aggregates, qualitative sim ulation generates explanations for the queries in Figure 7.2(c): 1. W hy chlorine (Cl) appears? W hen N O and CI2, in gas phase, collide w ith enough kinetic energy they break to produce NO Cl an d Cl. 2. Temperature effect? W hen reacting m olecules are heated, the population increase of high kinetic energy brings about an increase in the frequency of chem ical reaction. 3. Equilibrium? W hen high kinetic energy reacting m olecules interact, the populations of rem aining high kinetic energy reacting m olecules decrease, an d the populations of produced molecules increase. Consequently, the populations of high kinetic energy product m olecules increase. H ence the frequency of forw ard interaction decreases, and the frequency of reverse interaction increases. Finally, an equilibrium state is achieved. Electrolysis The process in w hich the application of an external source of voltage is used to cause chem ical changes is called electrolysis. Consider a physical system show n in Figure 7.3(a) in w hich the external voltage source changes w ater m olecules into hydrogen and oxygen gases. In the figure, tw o electrodes, w hich are connected to opposite term inals of a voltage source, are dipped into a contained water. W hen the circuit is closed, oxygen gas appears at the anode, and hydrogen gas appears at the cathode. 84 (a) (b) Battery r ^ i Cathode Anode f, Oxygen < --(> battery-e ( electron-flow) (Inod c-’ e*) (electron-flow) (cathode^, \ * * • ?-P \ J i m 2‘P , • ------ (oxidation) T 0 2 -ion> ^ H+ -io n y (reduction) (ionization) (c) “Why H, appears at the cathode?” electron-flow(battery, cathode) is active ionization(H20 , O2', H+) is active “ “ ' --------------------------- * “(ionizatic freq(electron-fiow) > zero 4,I+ TTpop(cathode-e) freq(ionization) > zero 1Tpop(^+-ion) reduction(cathode-e,H -ion, H2-p) is active freq(reduction) > zero ftpopit^-p) Figure 7.3: A situation involving electrolysis, (a) A n electrolysis of H 2O. (b) Particle aggregates and potentially active aggregate interactions identified by the PAI m ethod, (c) A n explanation for the appearance of hydrogen gas at the cathode. Electrolysis involves several interactions such as current-supply from a pow er source, current-flow, oxidation1 , reduction2, and ionization3. For the given system , the PAI m ethod finds out that these interactions are potentially active an d iden tifies various particle aggregates. These particle aggregates include electrons at the battery, electrons at the cathode, electrons at the anode, oxygen gases (O 2) on the surface of anode, hydrogen gases (H2) on the surface of cathode, w ater m olecules (H20 ) in the container, and oxygen ions (O2-) and hydrogen ions (H +) in the container (Figure 7.3(b)). 1A process of losing electrons. E.g. 2 0 z~ — * • O2 + 4e~. 2A process of gaining electrons. E.g. 2H+ + 2e_ — » H 2 . 3 A process of breaking of a molecule into two opposite ions. E.g. H 2 O — » 2H+ + O2 -. 85 (a) (b) “Why presfF) < pres(G)?” mass(H2) < mass(N2) Porous wall speed(H2) > speed(N2) freq(H2-in-F, F, G) > freq(N2-in-G, G, F) pop(H2-in-F) + pop(N2-in-F) < pop(H2-in-G) + pop(N2-in-G) pres(F) < pres(G) Figure 7.4: A situation involving gaseous diffusion, (a) G aseous diffusion of hydrogen and nitrogen, (b) Particle aggregates identified b y the PAI m ethod, (c) A n explanation for the pressure difference betw een the tw o cham bers. W ith m odels of such aggregate interactions and particle aggregates, qualita tive sim ulation generates an explanation for a query: 1. W hy H 2 appears? W hen the battery is on, electron flow from anode to cathode causes w ater to ionize into hydrogen ion, H +, and oxygen ion, O 2- (ionization). W hen hydrogen ions hit the cathode, they gain electrons, e~, from the cathode to form hydrogen gas, H 2, (reduction), and w h en oxygen hit the anode, they lose electrons to the anode to form oxygen gas (oxidation) (Figure 7.3(c)). G aseous D iffusion The process by w hich gases m ove through a porous w all is called gaseous diffusion. The porous w all prevents a m ass flow of gas b u t allow s m olecules to pass through. Consider the scenario show n in Figure 7.4(a) in w hich tw o cham bers (F an d G) are separated b y a porous wall, and each cham ber is initially filled w ith hydrogen and nitrogen at the sam e pressure and tem perature. For this exam ple, the PAI m ethod finds that diffusions of hydrogen and nitrogen betw een tw o cham bers are potentially active and th at four types of particle aggregates m ay exist, w hich are hydrogen an d nitrogen in both F and G. 86 These particle aggregates are show n in the second figure in Figure 7.4(b). W ith the m odels of such particle aggregates and an interaction diffusion, qualitative sim ulation provides an explanation for a query: 1. W hy does the pressure in G becom e greater? The frequency of diffusion is proportional to the speed of m olecules, and the speed is inversely p ro portional to the m ass. Since hydrogen is lighter than nitrogen, the speed of hydrogen in F is greater th an the speed of nitrogen in G. Therefore, the fre quency of diffusion of hydrogen from F to G is greater th an the frequency of diffusion of nitrogen from G to F. Consequently, the p opulation of both hydrogen and nitrogen in G becom es greater than the population of both hydrogen and nitrogen in F, hence the pressure of G becom es greater than the pressure of F (Figure 7.4(c)). 7.2 Other Dom ains To test the general applicability of our fram ew ork, w e selected several dom ains considerably different from each other such as electronics, econom ics, an d biol ogy. For these dom ains, w e investigated the characteristics of these dom ains as particulate system s and illustrate m odeling and sim ulation on selected exam ples. 7.2.1 The Electronics Dom ain A n electronic device consists of com ponents connected to each other. Electronic devices and com ponents are described b y a set of param eters such as resistance, voltage difference, current flow, etc. From the view of particulate system s, each com ponent has a collection of charge carriers such as electrons o r holes. These charge carriers have properties such as the types of charge (positive or negative) and the velocity of m ovem ent. The interactions causing changes to these electronic devices are m ainly flow of charges betw een the com ponents. 87 (a) Battery(B) (c) “Why charge increases?” closing-capacitor is active 1textent(charge-flov^electron,B,G)) \|/ 1 + 1 T o verlap-area(capaci tor) Varit pacitor lTextent(charge-flow(holes,B,F)) * (b) freq(charge-flow(electron,B,G)) > 0 1Tcharge(electron, G) electrons-B) « . electrons- q: charge-flow(holes,B,F) becomes active 4 ' freq(charge-flow(holes,B,F)) > 0 tt charge(noles,F) Figure 7.5: (a) A variable capacitor, (b) Particle aggregates identified by the PAI m ethod, (c) A n explanation of the increase in charge w h en the capacitor is being closed. In the P A /A I ontology, w e m odel the collections of charge carriers as particle aggregates and the charge-flows as aggregate interactions. For illustration, w e select an electronic device, a variable capacitor. In the follow ing, w e show a m odel of the capacitor represented in the P A /A I ontology and a sim ulation result w hich explains the functioning of a variable capacitor. Variable Capacitor A capacitor is an electronic device that consists of tw o conducting plates sepa rated by a sm all gap filled w ith dielectric. C apacitors are used to hold electric charge. The charge in the capacitor depends u p o n the voltage and capacitance. The capacitance depends upon the separation betw een the plates, overlapping area of tw o plates, and a dielectric constant. A fixed capacitor is the one w hose capacitance is fixed, and a variable capacitor is the one w hose capacitance can be varied by changing the overlapping area of tw o plates. C onsider the variable capacitor show n in Figure 7.5(a). Two plates (F and G) of a variable capacitor are connected to the term inals of a battery. Suppose w e 88 have a query "w hy is m ore charge gathered in the capacitor w hen w e close the capacitor." The PAI m ethod finds that charge-flows are potentially active betw een the term inals of the battery and plates of the capacitor w hen the capacitor is clos ing an d identifies particle aggregates such as electrons in G and holes in F (Figure 7.5(b)). W ith m odels of such particle aggregates an d interactions, the sim ulation generates an explanation for the query (Figure 7.5(c)): W hen closing the capacitor, the overlapping area betw een the plates increases, resulting in the increase in the extent of charge flow. Since this increase leads to additional charge flow of electrons an d holes to G and F, the populations of charge carriers in both plates increase. Consequently, the charge of the capacitor increases. 7.2.2 The Economics Dom ain Economics is a study of people's behavior in producing, exchanging, an d con sum ing the goods and services they desire, and the m ain actors in the economics are the producers, consum ers, and markets[23]. Producers and consum ers are the collections of individual producers and consum ers, and m arket is the place w here a collection of products are exchanged w ith money. For illustration, w e select a demand schedule4 in a com petitive m arket5. In the follow ing, w e show a m odel of the com petitive m arket represented in the PA /A I ontology and a sim ulation result w hich explains the form ation of a dem and schedule. 4 A demand schedule is a diagram that shows how the quantities of a product purchased over a certain time period change as its price changes [23], 5 A competitive market is the one composed of so many buyers and sellers that no one of them can influence the price or other conditions of sale[23]. 89 (c) “Demand schedule?” (a) Price(P) (b) / ' buying**'-* , •- consumers/ ■Uprice(product) consumers ■liopportunity-cost(buying-consumer,product) \J/Q + f products' "products***-.( purchased, / non-buying, . consumers/ tfpop(buying-consumer) \|/Q+ tl'freq(purchase) x J/Q + — > Quantity(P) 1?pop(products-purchased •Upop(products-in-market) Figure 7.6: (a) D em and schedule, (b) Particle aggregates identified by the PAI m ethod, (c) A n explanation of the increase in quantity purchased w hen the price of the product is decreasing. Dem and Schedule Viewing individual producers, consum ers, and products as particles, w e can m odel a competitive market of a specific product as a particulate system an d induce a dem and schedule (Figure 7.6(a)) of the product in a com petitive m arket. The interaction involved in this analysis is the act of purchasing. A consum er w ill bu y a product w hen the utility of the product is greater th an the opportunity- cost6 of the product. In analyzing the dem and schedule, the PAI m ethod finds a potentially active interaction, purchasing. It also finds particle aggregates w hich include products in the m arket, products purchased b y consum ers7, and its tw o ID PC-divided particle aggregates — consum ers w ho can b uy the product and consum ers w ho cannot buy the product. These particle aggregates are show n in Figure 7.6(b). The properties of them include populations of the particle aggregates, m arket price of the product, opportunity cost of a consum er for the product, utility of a consum er for the product, w ealth of a consum er, and the 6The next-best product or service that must be given up in order to obtain the product or service of one's choice[23]. 7The particle aggregate of producers and products manufactured by producers are not shown here. These are required for analyzing supply schedule. 90 frequency of purchasing. W ith these m odels, qualitative sim ulation generates an explanation for the increase in the quantity-purchased w hen the price goes dow n, form ing the dem and curve (Figure 7.6(c)): If the price of a product decreases, the opportunity cost of consum ers for the product decreases, leading to the increase in the population of custom ers w ho can buy the product. Consequently, the frequency of purchasing increases, w hich m eans an increase in the quantity purchased in the m arket. 7.2.3 The Biology Dom ain Biology involves fields such as cells, organism s, reproduction, genetics, evolu tion, and ecology [37]. A m ong them , ecology, cells, and organism s can be m od eled as particulate system s since ecology is the study of changes of populations of living organism s in environm ents, and m ost of the physiological processes w ithin cells and organism s are chem ical in nature. These physiological processes include photosynthesis, the potassium-sodium pump model, and protein synthesis. We select the potassium -sodium m odel to m odel and perform sim ulation using the P A /A I ontology. In the following, w e show a m odel of the potassium - sodium p um p and a sim ulation result w hich explains the functioning of the m odel. The Potassium Pump M odel C onsider the potassium -sodium pu m p m odel show n in Figure 7.7(a). This m odel is the one that biologists propose to explain living cells' m aintenance of low concentration of sodium , N a+, and high concentration of potassium , K+, w hich is essential for generating nervous im pulses and heartbeats. As in m any physiological processes, the potassium -sodium pum p m odel consists of a set of chem ical reactions such as com position, dissociation, diffusion, and conversion. 91 (b) conversion-out Na -K PUMP composition-out K+(out) Net passive diffusion Metabolic drive Net passive diffusion K +(in) y dissociation-in; <KX(outj/’ — diffusion-m " ^_X(in)y (c) I conversion-in <Y(outy> diffusion-out^ C.Y(in)y **'lll^>HCNaY(ouO>*—C N a Y ( i i ] ' /}i c v n /'isitin n -Stilt / . / i m n / i n V m t <Na+(out)/dissociation-out composition-in ( [Na+ (inp “Why is pop(K+(in)) increasing?” pop(K +(out)) > 0 p op (X (ou t)) > 0 \ / com position -ou t is active \J/I+ ftpop (K X (out)) diffusion -in b eco m es active 4,1+ fTpop(KX(in)) 'J' dissociation-in becomes active V V 1Tpop(K+(in)) 1Tpop(X(in)) Figure 7.7: (a) The potassium -sodium pu m p m odel, (b) Particle aggregates and aggregate interactions identified by the PAI m ethod, (c) A n explanation of the increase in concentration of potassium ions (K+) inside cells. For this m odel, the PAI m ethod identifies various particle aggregates and potentially active interactions. These particle aggregates and aggregate interac tions are show n in Figure 7.7(b). W ith the m odel of these particle aggregates and aggregate interactions, qualitative sim ulation generates an explanation for the m aintenance of high concentration of potassium inside cells as show n in Figure 7.7(c). A carrier substance, X, com bines w ith potassium ions, K+, on the outer surface of the cell m em brane, form ing a new com pound KX. KX then diffuses passively across the m em brane following its ow n concentration gradient. O n the inner surface of the m em brane, KX dissociates, releasing potassium ions, K+, into the cell. 92 7.3 D iscussion In this chapter, to evaluate the applicability of our fram ew ork, w e achieved an in-depth investigation of a particular dom ain, chemistry, based on a college level textbook. We found that about 50% of the exam ples in the textbook are of partic ulate system s, and out of the 50%, about 70% can be handled by our m ethod. In addition, w e exam ined several other dom ains to evaluate the generality of the proposed fram ew ork. The selected dom ains included biology, electronics and economics. We m odeled and sim ulated several exam ples from these dom ains. We found that our m ethod can be w ell applied to som e of the problem s from these dom ains. The results of the sim ulations on those exam ples are sum m arized in A ppendix B. By investigating the exam ples w hich are particulate system s b u t cannot be handled by our m ethod, w e found several lim itations including: 1. Our method lacks a finer-grained quantization or quantitative information: O ur reasoning m ethod is based on the sim ple quantization of num bers by their signs. But som e of the exam ples in chem istry require finer-grained quanti zation, such as order-of-m agnitude reasoning[31] (for differentiating strong and w eak acids) and relative m agnitudes (for m ultistage equilibria am ong w eak acid and base) and integration w ith num erical inform ation (acid-base titration). 2. Our method lacks a sophisticated geometric reasoner: O ur m ethod does not include consideration of geom etrical inform ation. Geom etric reasoning is one of the least developed areas in qualitative physics[16]. H ow ever, to explain the functioning of electronic devices, w e need to consider concepts such as electric field and direction of velocity. In the chem istry dom ain, exam ples such as T hom pson's effect, prism effects, concentration gradient of diffusion also require geom etrical inform ation. 93 3. Our method lacks an individual particle based reasoner: O ur reasoning is p er form ed based on particle aggregates, ignoring irregular and transitory m otions of individual particles. Therefore, our m ethod cannot explain physical phenom ena such as random w alks of fluid particles an d diffusion of dye. 94 Chapter 8 D iscussion In this chapter, w e sum m arize the w ork described in this thesis, discuss future w ork, and conclude w ith the significance of this research. 8.1 Summary This thesis has dem onstrated how to m odel an d sim ulate particulate system s to explicate the deeper causal theories based u p o n constituent particles. M ajor contributions of the thesis include: 1. We have developed m odeling prim itives for particulate system s and a representation language w hich facilitates the qualitative reasoning of par ticulate system s. 2. We have developed the PAI m ethod that finds qualitatively im portant par ticle aggregates relevant to reasoning, and the IDPC m ethod that classifies particles based on their participation in interactions. 3. We have investigated the characteristics of aggregate interactions and iden tified the types of relations to be generated for particle aggregates of clas sified particles. 95 4. We have identified the nature of kinetic energy redistribution as w ell as its effects in therm odynam ic system s and developed a w ay to m odel the effects of redistribution. 5. We have developed m odels for particle aggregates, aggregate interactions, and interconnecting theories, in QP theory language, an d im plem ented a system to perform sim ulation on exam ples from various dom ains such as chemistry, biology, electronics, and economics. 8.2 Future Research The lim itations discussed in the previous chapter suggest several im portant directions for future research: 1. Enhanced quantization: We plan to enhance our system by integrating order- of-m agnitude reasoning[31] and num erical sim ulation to analyze physical phenom ena such as strong and w eak acids, m ultistage equilibria am ong w eak acid and bases, and acid-base titration. 2. Geometrical reasoner: We plan to enhance our system to capture the detailed geom etrical changes of individual particles to analyze random w alks of fluid particles and velocities of electric charges in an electric field. 3. Model Selection: We plan to develop a m odeling m ethod that selects a relevant and parsim onious m odel of a particulate system based on the analysis of queries. 4. Learning: We plan to extend our earlier research on learning m acroscopic theories of physical phenom ena[32] by incorporating m icroscopic theories on particles to validate and extend the learned m acroscopic theories. 96 8.3 Significance of the Research Q ualitative reasoning w ith particles is of considerable im portance in the u n derstanding and explication of m any physical phenom ena. Exam ples include electricity and conduction, radioactive decay, and capillary action in physics; catalytic reactions, chain reactions, ionization and electrolysis, dissociation and solubility in chem istry; im m unization m echanism , blood circulation, grow th of cancerous cells in biology and m edicine; and so forth. The significance of this research lies in the scope of problem s w hich can be analyzed w ith the proposed analysis m ethod and in the enhancem ent of the perform ance of earlier qualitative reasoning system s b y explicating deeper causal m echanism s. Recent trends in evaluating qualitative sim ulation m ethods puts em phasis on its potential applications!!]. Q ualitative reasoning based on particle behaviors is useful in applications that require deeper explanations. For exam ple, intelligent tutoring system s of advanced scientific concepts in chem istry m ust involve a qualitative description of the kinetic theory of particles and its use in the ex planation of diverse phenom ena like chem ical reaction, osmosis, evaporation, electrolysis, chain reaction, catalytic action, and so on. Similarly, expert system s that m onitor steam plants and nuclear reactors m ust be equipped w ith detailed theories in order to provide superior perform ance. For exam ple, the detailed theories on particle's behaviors can be used for reasoning about the nature of the physical phenom ena and the factors that influence them . This thesis presents a step tow ard these goals. 97 A ppendix A D etails of the Escape Example PAIer is an im plem entation of the PAI m ethod. It is an ATMS[12] based produc tion system w hich takes the m odel for aggregate interactions, initially available particle aggregates, and the P S /IP m odel. Then it produces the P-I diagram . W hile generating the P-I diagram , PAIer identifies particle aggregates that are new ly introduced by active interactions, and, as necessary, classifies particles in the existing particle aggregates to distinguish interacting from non-interacting particles, and generates their relations. W hen all the particle aggregates are available, w e construct m odels for par ticle aggregates and aggregate interactions conform ing to the QPE language. QPE takes m odels of particle aggregates, aggregate interactions, particle redis tributions, interconnecting theories, and scenario description. T hen it generates envisionm ent w hich describe the behavior of the given physical system . In terpretation of the envisionm ent provides the explanations for various queries show n in this thesis. T hroughout this thesis, a physical system , a contained w ater, is analyzed to provide an answ er to the query regarding the tem perature drop du rin g evapo ration. In this A ppendix, w e show the details of the program ru n of the PAIer and QPE sim ulation on this example. 98 A .l The PAI M ethod In this section, w e describe the system inputs, the program ru n and the outputs of PAIer on ecape exam ple. A.1.1 System Inputs System inputs include the m odel for particle escape, initially existing particle aggregates and the P S /IP netw ork. A M odel for Escape: AI '(escape ?p) :individual '((PA ?p) (substance ?p ?sub) (PS-of ?p ?ps) (PS ?ps) (PS ?ps2)) :IP '((IP ?ip) (permit-phase-transition ?ip (source-ps ?psl) (dest-ps ?ps2))) :property-condition '((phase ?p liquid)) :quantity-condition '(((KE ?p) ((BE ?sub) +infinity))) :delete-list '((PA ?p)) :add-list ' (((PA ?p2) (PS-of ?p2 ?ps2) (substance ?p2 ?sub) (phase ?p2 gas) ((KE ?p2) (0 +infinity)))) :aggregate-relations '((quantity frequency) (greater-than (a frequency) zero) (qprop+ frequency (extent ?ip)) (qprop+ frequency (population ?p))) :influences '((I- (population ?p) (A frequency)) (1+ (population ?p2) (A frequency)))) 99 In itially A vailable Particle A ggregates: O nly one particle aggregate for liquid particles exist initially. (PA '(PA pi) :PS '((PS-of pi psl)) :property '((substance pi water) (phase pi liquid)) .■quantity ' ( ( (KE pi) (0 -(-infinity) ) ) ) PS/IP N etw ork: (PS-IP-models '((PS ps-liquid) (PS ps-gas) (IP ip-escape) (permit-phase-transition ip-escape (source-ps ps-liquid) (dest-ps ps-gas)))) A.1.2 PA Identification D uring PAIer run, it classifies particles in the liquid particle aggregate (Pi) into tw o sub-particle aggregates ( P l - 9 3 6 6 , P l - 9 3 6 5 ) according to kinetic energy, generates their relations w ith existing particle aggregates (Type A and Type B), and identifies one new particle aggregate (P 2-93 68) for gas particles. ;;; A PA is classified ... ;;; From: <PA => 1 (PA Pl)> ;;; To : <PA => 3 (PA Pl-9366)> <PA => 2 (PA Pl-9365)> ;;; Population relations (Type A) are generated ... ;;; (QPROP+ (POPULATION (PA PI)) (POPULATION (PA Pl-9365))) ;;; (QPROP+ (POPULATION (PA PI)) (POPULATION (PA Pl-9366))) ;;; Average quantity relations (Type B) are generated ... ;;; (QPROP- (KE (PA PI)) (POPULATION (PA Pl-9365))) ;;; (QPROP+ (KE (PA PI)) (POPULATION (PA Pl-9366))) ;;; A new PA is identified ... ; ; , - <PA => 4 (PA P2-9368)> A t the end of PAIer run, the following particle aggregates are available. 100 PARTICLE AGGREGATE ==> 1 (PA PI) (PS-OF PI PS-LIQUID) (PARTICLE PI) (SUBSTANCE PI WATER) (PHASE PI LIQUID) ((KE PI) (0 +INFINITY)) (QPROP+ (KE (PA Pi)) (POPULATION (PA Pl-9366))) (QPROP- (KE (PA Pl|) (POPULATION (PA Pl-9365))) (QPROP+ (POPULATION (PA PI)) (POPULATION (PA Pl-9366))) (QPROP+ (POPULATION (PA Pi)) (POPULATION {PA Pl-9365))) PARTICLE AGGREGATE ==> 2 PA-name : (PA Pl-9365) Particle System : (PS-OF Pl-9365 PS-LIQUID) property : (PARTICLE Pl-9365) (SUBSTANCE Pl-9 3 65 WATER) (PHASE Pl-9 3 65 LIQUID) quantity : ((KE Pl-9365) (0 (BE WATER))) aggregate-relations : NIL PA-name : Particle System : property : quantity : aggregate-relations : PARTICLE AGGREGATE ==> 3 PA-name Particle System property quantity aggregate-relations (PA Pl-9366) (PS-OF Pl-9366 PS-LIQUID) (PARTICLE Pl-9366) (SUBSTANCE Pl-9366 WATER) (PHASE Pl-93 66 LIQUID) ((KE Pl-9366) ((BE WATER) NIL (■INFINITY) ) PARTICLE AGGREGATE ==> 4 PA-name Particle System property quantity aggregate-relations (PA P2-9368) (PS-OF P2-9368 PS-GAS) (PHASE P2-9368 GAS) (SUBSTANCE P2-93 68 WATER) (PARTICLE P2-9368) ((KE P2-9368) (0 +INFINITY)) NIL A.1.3 System Output As an output, PAIer generates the P-I diagram as follows: 101 << P-state list >> [State 1] PA(2) PA(3) [State 2] PA(2) PA(4> [State 3] PA(2) PA(3) PA(4) « I-trans list >> [Trans 1] AI(l) leads from [State 1] to [State 2 3] [Trans 2] AI(1) leads from [State 3] to [State 2 3] From the P-I diagram , som e queries related w ith the tim e evolution of p ar ticles can be answ ered. For exam ple, from [Trans 1], w e know that [State 2 ] in w hich gas particles exist is the resulting state of [ State 1 ] in w hich gas particles do not exist. In other w ords, the gas particle is generated by active interaction escape. A.2 QPE Sim ulation In this section, w e describe the inputs to QPE, w hich are dom ain m odels and system m odels, and the output, w hich is an envisionm ent. A.2.1 System Inputs D om ain M odel A dom ain m odel is the general know ledge on the dom ain of contained liquids and particle escape that are required for sim ulation. It includes various quanti ties required for the P A /A I ontology, syntactic artifacts required for generating particle aggregate instances, the general m odel of particle aggregates, the m odel of CL-level objects such as contained-liquid, kinetic energy redistribution com pensatory processes, process definition of particle escape, etc. ;;; 1. Important quantities of the PA/AI ontology (defquantity-type population individual) (defquantity-type KE individual) [defquantity-type extent individual) (defquantity-type frequency individual) 102 ; ; ; 2 . Some predicates (defpredicate non-negative-quantity (quantity ?self) (not (less-than (A ?self) ZERO)}) (defpredicate positive-quantity (quantity ?self) (greater-than (A ?self) ZERO)) 3. Important physical entities for the PA/AI ontology. (defentity ip (positive-quantity (extent ?self))) (defentity aggregate-interaction (non-negative-quantity (frequency ?self))) (defentity particle-aggregate (non-negative-quantity (population ?self)) (positive-quantity (KE ?self))) ;;; 4. PAs as individual views (both defperspective and defview are required ; ; ; for envisionment). (defperspective (generate-PAs ’name ?ps ?subs ?ph ?int) individuals ((’name :type particle) (?ps :type ps) (?subs :type substance) (?ph :type phase) (?int :type interval :conditions (form-a-PA ?name ?ps ?subs ?ph ?int))) relations ((PA ?name ?ps ?subs ?ph Pint) (particle-aggregate (PA ’name ?ps ?subs ?ph ?int))>) (defview (part-aggr (PA ’name ?ps ?subs ?ph ?int)) individuals ((?name :type particle) (?ps :type ps) (?subs :type substance) !?ph :type phase) (?int :type interval :conditions (form-a-PA ’name ?ps ?subs ?ph ?int))) quantityconditions ((greater-than (A (population (PA ?name ?ps ?subs ?ph ?int))) zero)) relations (((v-i (PA ?name ?ps ?subs ?ph ?int)) ?self))) ;;; 5. Part-part relations due to kinetic energy redistributions. (defperspective (PA-relationships ?loKEp ?hiKEp ?avrKEp) individuals ((?loKEp :type particle-aggregate :form (PA ?pl ?ps ?sub ?ph (KE-int zero (BE ?sub)))) (?hiKEp :type particle-aggregate :form (PA ?p2 ?ps ?sub ?ph (KE-int (BE ?sub) infinity))) (?avrKEp :type particle-aggregate .•form (PA ?p3 ?ps ?sub ?ph (KE-int zero infinity)))) relations (;;; population relationships (Q= (population ?avrKEp) (+ (population ?loKEp) (population ?hiKEp))) ;;; average KE relationships (qprop (KE ?avrKEp) (population ?hiKEp)) ;;; more restrictions (ordered-correspondence {(a (population ?loKEp)) zero) ((a (population ?hiKEp)) zero)))) ;;; 6. Interconnecting theories (defquantity-type amount individual) (defquantity-type temperature individual) (defview (contained-stuff ?cs) individuals ((?avrKEp :type part-aggr :form (PA ?p ?ps ?sub ?st (ke-int zero infinity)) conditions ((v-i PavrKEp) ?vi-avr-p)) (?can :type container conditions (can-hold ?can ?p)) (?cs :bind (C-S ?sub ?st ?can))) quantityconditions ((active ?vi-avr-p)) relations (((v-i ?cs) ?self) ;; Interconnecting theories on amount and temperature (quantity (amount ?cs)) (qprop (amount ?cs) (population ?avrKEp)) (correspondence ((a (amount ?cs)) zero) ((a (population ?avrKEp)) zero)) (quantity (temperature ?cs)) (qprop (temperature ?cs) (ke ?avrkep)) 104 (correspondence {(a (temperature ?cs)) zero) ( (a (ke ?avrKEp)) zero)))) 7. Redistributory compensation processes. There exist four types of compensatory processes according to the types of interactions, such as upper/lower thresholding, and entering/exiting interactions. (defprocess (redistributory-compensation-upper-exit (RC-UEX ?hiKEp ?loKEp)) individuals ((?hiKEp :type part-aggr :form (pa ?pl ?ps ?sub ?phase (KE-int (BE ?sub) infinity))) (?loKEp :type part-aggr :form (pa ?p2 ?ps ?sub ?phase (KE-int zero (BE ?sub)))) (?pi :conditions (upper-thresholding ?pi) (exiting-from ?pi ?hiKEp))) quantityconditions ((active ?pi)) relations (((p-i (RC-UEX ?hiKEp ?loKEp)) ?self) (quantity frequency) (greater-than (a frequency) zero) (less-than (a frequency) (a (frequency ?pi)))! influences ((1+ (population (PA ?pl ?ps ?sub ?phase (KE-int (BE ?sub) infinity))) (a frequency)) (I- (population (PA ?p2 ?ps ?sub ?phase (KE-int zero (BE ?sub)))) (a frequency)))) (defprocess (redistributory-compensation-upper-entering (RC-UEN ?hiKEp ?loKEp)) individuals ((?hiKEp :type part-aggr :form (pa ?pl ?ps ?sub ?phase (KE-int (BE ?sub) infinity))) (?loKEp :type part-aggr :form (pa ?p2 ?ps ?sub ?phase (KE-int zero (BE ?sub)))) (?pi :conditions (upper-thresholding ?pi) (entering-to ?pi ?hiKEp))) quantityconditions ((active ?pi)) relations (((p-i (RC-UEN ?hiKEp ?loKEp)) ?self) (quantity frequency) (greater-than (a frequency) zero) (Xess-than (a frequency) (a (frequency ?pi)))) influences ((I- (population (PA ?pl ?ps ?sub ?phase (KE-int (BE ?sub) infinity))) (a frequency)) (1+ (population (PA ?p2 ?ps ?sub ?phase (KE-int zero (BE ?sub)))) (a frequency)))) (defprocess (redistributory-compensation-lower-exit (RC-LEX ?hiKEp ?loKEp)) individuals ((?hiKEp :type part-aggr :form (pa ?pl ?ps ?sub ?phase (KE-int (BE ?sub) infinity))) (?loKEp :type part-aggr :form (pa ?p2 ?ps ?sub ?phase (KE-int zero (BE ?sub)))) (?pi :conditions (lower-thresholding ?pi) (exiting-from ?pi ?loKEp))) quantityconditions ((active ?pi)) relations (((p-i (RC-LEX ?hiKEp ?loKEp)) ?self) (quantity frequency) (greater-than (a frequency) zero) (less-than (a frequency) (a (frequency ?pi)))) influences ((I- (population (PA ?pl ?ps ?sub ?phase (KE-int (BE ?sub) infinity))) (a frequency)) (1+ (population (PA ?p2 ?ps ?sub ?phase (KE-int zero (BE ?sub)))) (a frequency)))) (defprocess (redistributory-compensation-lower-entering (RC-LEN ?hiKEp ?loKEp)) individuals ((?hiKEp :type part-aggr :form (pa ?pl ?ps ?sub ?phase (KE-int (BE ?sub) infinity))) (PloKEp :type part-aggr :form (pa ?p2 ?ps ?sub ?phase (KE-int zero (BE ?sub)))) (?pi :conditions (lower-thresholding ?pi) (entering-to ?pi ?loKEp))) quant i tycondi t i ons ((active ?pi)) relations <((p-i (RC-LEN ?hiKEp ?loKEp)) ?self) (quantity frequency) (greater-than (a frequency) zero) (less-than (a frequency) (a (frequency ?pi)))) influences ((1+ (population (PA ?pl ?ps ?sub ?phase (KE-int (BE ?sub) infinity))) (a frequency)) (I- (population (PA ?p2 ?ps ?sub ?phase (KE-int zero (BE ?sub)))) (a frequency)))) ;;; 7. A model for particle escape. (defprocess (escape (ESC ?pa-liq ?p2 ?ip)) individuals ((?pa-liq :type part-aggr :form (PA ?pl ?psl ?sub liquid (ke-int (BE ?sub) infinity)) :conditions {{v-i ?pa-liq) ?vi-pa-liq)) (?p2 :conditions (PA ?p2 ?ps2 ?sub gas ?int2)) (?ip :type ip :conditions (permit-phase-transition ?ip (source-ps ?psl) (dest-ps ?ps2)))) quanti tycondi ti ons ((active ?vi-pa-liq) (greater-than (A (extent ?ip)) zero)) relations (({p-i (ESC ?pa-liq ?p2 ?ip)) ?self) (quantity frequency) (greater-than (a frequency) zero) (qprop+ frequency (extent ?ip)) (qprop+ frequency (population ?pa-liq)) ;; interaction type (upper-thresholding ?self) (exiting-from ?self ?pa-liq) (entering-to ?self (PA ?p2 ?ps2 ?sub gas ?int2))) influences ((I- (population (PA ?pl ?psl ?sub liquid (KE-int (BE ?sub) infinity))) (A frequency)) (1+ (population (PA ?p2 ?ps2 ?sub gas ?int2)) (A frequency)))) System M odel A system m odel describes a specific situation u n der consideration. In the p ar ticulate system s, it includes the structural description of the situation, the infor m ation on the particle aggregates identified during PAIer run, and the P S /IP netw ork. ;;; 1. Structural description (assertq (substance water)) (assertq (phase liquid)) (assertq (phase gas)) (assertq (container F)) (assertq (can-hold F avrKEp)) ;;; 2. PAs identified during the PAI method. (assertq (form-a-PA hiKEp ps-liq water liquid (KE-int (BE water) infinity))) (assertq (form-a-PA loKEp ps-liq water liquid (KE-int zero (BE water)))) (assertq (form-a-PA avrKEp ps-liq water liquid (KE-int zero infinity))) (assertq (form-a-PA gas-p ps-gas water gas (KE-int zero infinity))) ;; 3. PS/IP information (assertq (ps ps-liq)) (assertq (ps ps-gas)) (assertq (ip ip-escape)) (assertq (permit-phase-transition ip-escape (source-ps ps-liq) (dest-ps ps-gas))) A.2.2 System Output D uring sim ulation, QPE finds out all the process and view instances, an d gener ates envisionm ent w hich is the set of consistent com bination of active view and process instances. V iew and Process Instances Five types of view instances are available w hich include a PA for liquid particles, PAs for high and low kinetic energy particles, a PA for gas particle, finally a PA 108 for contained water. Two types of process instances are available for the particle escape and a kinetic energy redistributory com pensation process. I. View instances: VXO = PART-AGGR (PA(HIKEP, PS-LIQ, WATER, LIQUID, KE-INT (BE (WATER) .INFINITY) )) VII = PART-AGGR (PA (LOKEP, PS-LIQ, WATER, LIQUID, KE-INT ( ZERO, BE (WATER) ) ) ) VI2 = PART-AGGR(PA(AVRKEP,PS-LIQ,WATER,LIQUID,KE-INT(ZERO,INFINITY))) VI3 = CONTAINED-STUFF(C-S(WATER,LIQUID,F)) VI4 = PART-AGGR (PA (GAS-P, PS-GAS,WATER, GAS, KE-INT (ZERO, INFINITY) ) ) II. Process instances: PIO = ESCAPE(ESC(PA(HIKEP,PS-LIQ,WATER,LIQUID,KE-INT(BE(WATER),INFINITY)), GAS-P,IP-ESCAPE)) PIl = REDISTRIBUTORY-COMPENSATION-UPPER-EXIT (RC-UEX (PA(HIKEP, PS-LIQ, WATER, LIQUID, KE-INT (BE (WATER) , INFINITY) ) , PA(LOKEP,PS-LIQ,WATER,LIQUID,KE-INT(ZERO,BE(WATER))))) E nvisionm ent Envisionm ent describes the behavior of a given physical system w ith a state transition diagram . Each state is defined by a set of active view and process instances and their quantity values. For simplicity, only the activities of the instances are show n below. I. States: VI0 VII VI2 VI3 VI4 PIO PIl SO I I I I I I I SI A A A A I A A S2 I I I I A I I S3 A A A A A A A II. Transitions: ((SI (S3) (S2) ) (S3 (S 2))) Explanation for Temperature Drop To answ er the query on the tem perature drop in the evaporation, w e need to choose a desired state from envisionm ent. We select the final state, S3, since all 109 the particle and interaction instances are active in the state. In S3, the tem pera ture and the am ount of contained w ater are decreasing since the average kinetic energy and the population of liquid particles are decreasing. These decreases are due to the decrease in the high kinetic energy liquid particles resulting from ac tive interaction escape. The following is the p art of envisionm ent that is required for the explanation. Ds[AMOUNT(C-S(WATER,LIQUID,F))]=-l Ds[TEMPERATURE(C-S(WATER,LIQUID,F))]=-l Ds[KE(PA(AVRKEP,PS-LIQ,WATER,LIQUID,KE-INT(ZERO,INFINITY)))]=-! Ds[KE(PA(GAS-P,PS-GAS,WATER,GAS,KE-INT(ZERO,INFINITY)))]=0 Ds[KE(PA(HIKEP,PS-LIQ,WATER,LIQUID,KE-INT(BE(WATER).INFINITY)))]=0 Ds [ POPULATION (PA (AVRKEP, PS-LIQ, WATER, LIQUID, KE-INT ( ZERO, INFINIT?) ) ) ]=-l DS [POPULATION (PA (GAS-P, PS-GAS, WATER, GAS, KE-INT (ZERO, INFINITY) ) ) ] =1 Ds[POPULATION(PA(HIKEP,PS-LIQ,WATER,LIQUID,KE-INT(BE(WATER) , INFINITY) ) )]=-1 Ds[POPULATION(PA(LOKEP,PS-LIQ,WATER,LIQUID,KE-INT(ZERO,BE(WATER))))]=-l Ds[EXTENT(IP-ESCAPE)]=0 Ds[FREQUENCY(PIO)]=-1 Ds[FREQUENCY(PIl)]=0 Ds[KE(PA(LOKEP,PS-LIQ,WATER,LIQUID,KE-INT(ZERO,BE(WATER))))]=0 The causal chains that provide the above results are the qualitative propor tionalities and direct influences. The following is the p a rt of such qualitative relationships generated during QPE simulation. Qprop(AMOUNT(C-S(WATER,LIQUID, F)) , POPULATION (PA (AVRKEP, PS-LIQ, WATER, LIQUID, KE-INT(ZERO, INFINITY) ) ) ) Qprop(TEMPERATURE(C-S(WATER,LIQUID,F)) , KE(PA(AVRKEP,PS-LIQ,WATER,LIQUID,KE-INT(ZERO,INFINITY)))) Qprop (POPULATION (PA (AVRKEP, PS-LIQ, WATER, LIQUID, KE-INT(ZERO, INFINITY) ) ) , POPULATION(PA(LOKEP,PS-LIQ,WATER,LIQUID,KE-INT(ZERO,BE(WATER))))) Qprop (POPULATION (PA (AVRKEP, PS-LIQ, WATER, LIQUID, KE-INT(ZERO, INFINITY) ) ) , POPULATION(PA(HIKEP,PS-LIQ,WATER,LIQUID,KE-INT(BE(WATER).INFINITY)))) Qprop (KE( PA (AVRKEP, PS-LIQ, WATER, LIQUID, KE-INT(ZERO, INFINITY) ) ) , POPULATION(PA(HIKEP,PS-LIQ,WATER,LIQUID,KE-INT(BE(WATER),INFINITY)))) I- (POPULATION(PA(LOKEP, PS-LIQ, WATER, LIQUID, KE-INT(ZERO, BE (WATER) ) ) ) , A [FREQUENCY(PIl)]) 1+ (POPULATION (PA (HIKEP, PS-LIQ, WATER, LIQUID, KE-INT (BE (WATER) , INFINITY) ) ) , 110 A[FREQUENCY(PIl) ] ) I-(POPULATION!PA(HIKEP,PS-LIQ,WATER,LIQUID,KE-INT(BE(WATER),INFINITY))), A[FREQUENCY(PIO)]) 1+ (POPULATION (PA (GAS-P, PS-GAS , WATER, GAS, KE-INT (ZERO , INFINITY) ) ) , A [FREQUENCY(PIO)]) U sing the above quantities and their causal relations, an explanation for the tem perature drop is constructed as follows: <<Causal chain 1 » When PIO (particle escape) is active: I- (POPULATION (PA (HIKEP, PS-LIQ, WATER, LIQUID, KE-INT (BE (WATER) , INFINITY) ) ) , A [FREQUENCY(PIO)]) Ds [POPULATION (PA (HIKEP, PS-LIQ, WATER, LIQUID, KE-INT(BE (WATER) ,INFINITY) ) ) ]=-l «Causal chain 2>> Qprop(KE(PA(AVRKEP,PS-LIQ,WATER,LIQUID,KE-INT(ZERO,INFINITY) ) ) , POPULATION(PA(HIKEP,PS-LIQ,WATER,LIQUID,KE-INT(BE(WATER),INFINITY)))) DS[KE(PA(AVRKEP,PS-LIQ,WATER,LIQUID,KE-INT(ZERO,INFINITY)))]=-1 <<Causal chain 3>> When VI3 (interconnecting theory) is active: Qprop (TEMPERATURE (C-S (WATER, LIQUID, F) ) , KE(PA(AVRKEP,PS-LIQ,WATER,LIQUID,KE-INT(ZERO,INFINITY)))) Ds[TEMPERATURE(C-S(WATER,LIQUID,F))]=-1 W hen particle escape is active, the population of high kinetic en- ergy particle aggregate decreases (Causal chain 1) w hich results in a decrease in the average kinetic energy of liquid particles (Causal chain 2). According to the interconnecting theory involving contained- liquid, the tem perature of the liquid is proportional to the average kinetic energy of liquid particles (Causal chain 3). Since the average kinetic energy decreases, the tem perature of the liquid decreases. In this appendix, w e have described the details of the program ru n of the PAIer and QPE sim ulation on escape exam ple — their system input, o u tp u t and program run, and show ed an explanation for the query about the tem perature drop during evaporation. I l l Appendix B Summary of Examples In this chapter, w e sum m arize the results of sim ulations on the com plete exam ples described in this thesis. B .l Examples from the Chemistry Dom ain Table B.l: The sum m ary of sim ulations on the exam ples from the chem istry dom ain.______________________________________________________________ Ex Initially available PAs IDPC- classified PAs Relations generated PAI- identified PAs Q ueries answ ered Phase transitions in a contained w ater liq-p hiKEp loKEp Q+(pop(liq-p),pop(hiKEp)) Q+(pop(liq-p),pop(loKEp)) Q+(KE(liq-p),pop(hiKEp)) Q-(KE(liq-p),pop(loKEp)) gas-p Tempera ture- drop Tem perature- effect Phase transitions in a contained solution solv-p salt-p hiKE-solv-p loKE-solv-p Q+(pop(solv-p),pop(hiKE-solv-p)) Q+(pop(solv-p),pop(loKE-solv-p)) Q+(KE(solv-p),pop(hiKE-solv-p)) Q-(KE(solv-p),pop(loKE-solv-p)) gas-p C oncentration- effect Tem perature- effect Forw ard chem ical reaction N O -p C l2-P hiKE-NOp loKE-NOp hiKE-Cl2p I0KE-CI2P Q +(pop(N O-p)/pop(hiKE-NOp)) Q+(pop(NO-p),pop(loKE-NOp)) Q+{KE(NO-p),pop(hiKE-NOp)) Q-(KE(NO-p),pop(loKE-NOp)) Q +(pop(Cl2-p),pop(hiKE-Cl2p)) Q +(pop(Cl2-p),pop(loKE-Cl2p)) Q+(KE(Cl2-p),pop(hiKE-Cl2p)) Q-(KE(Cl2-p),pop(loKE-Cl2p)) N OCL-p Cl-p Chem ical- reaction Tem perature- effect 112 Table B.2: The sum m ary of sim ulations on the exam ples from the chem istry dom ain (continued). Ex Initially available PAs IDPC- classified PAs R elations generated PAI- identified PAs Q ueries answ ered Forw ard and reverse chem ical reaction N O -p Cl2-p hiKE-NOp loKE-NOp hiKE-Cl2p loKE-Cl2p hiKE-NOClp loKE-NOCIp hiKE-Clp loKE-Clp Q +(pop(NO-p),pop(hiKE-NOp)) Q+(pop(NO-p),pop(loKE-NOp)) Q+(KE(NO-p),pop (hiKE-NOp)) Q-(KE(NO-p),pop(loKE-NOp)) Q+(pop(Cl2-p)/pop(hiKE-Cl2p)) Q +(pop(Cl2-p),pop(loKE-Cl2p)) Q+(KE(Cl2-p),pop(hiKE-Cl2p)) Q-(KE(Cl2-p),pop(loKE-Cl2p)) Q +(pop(NOCl-p),pop(hiKE-NOClp)) Q+(pop(NOCl-p),pop(loKE-NOClp)) Q+(KE(NOCl-p),pop(hiKE-NOClp)) Q-(KE(NOCl-p),pop (loKE-NOCIp)) Q+(pop(Cl-p),pop(hiKE-Clp)) Q+(pop(Cl-p),pop(loKE-Clp)) Q+(KE(Cl-p)/pop(hiKE-Clp)) Q-(KE(Cl-p),pop(loKE-Clp)) NOCL-p Cl-p Chem ical- reaction Tem perature- effect E quilibrium Electrolysis h 2o battery-e cathode-e anode-e,H 2 O j U l O 2- H 2 appears G aseous diffusion h 2-f n 2-g H 2-G n 2-f Pressure- difference 113 B.2 Examples from Other Dom ains Table B.3: The sum m ary of sim ulations on the exam ples from other dom ains. Ex Initially available PAs IDPC- classified PAs Relations generated PAI- identified PAs Queries answ ered Variable capacitor hole-B electron-B hole-F electron-G Functioning- of-capacitor D em and schedule in a com petitive m arket consum er product Buy-c noBuy-c Q +(pop(consumer),pop(Buy-c)) Q+(pop(consumer),pop(noBuy-c)) cons- product D em and- schedule The potassium sodium p um p m odel (No IDPC classification assum ed) K+ (out) N a+ (in) X(out) KX(out) KX(in) K+ (in),etc M aintaining- high K + . 114 Reference List [1] Computational Intelligence: Special Issue on Qualitative Physics. M ay 1992. [2] S. A danki, R. Crem onini, and J. Penberthy. G raphs of m odels. Artificial Intelligence, 1991. [3] F. G. A m ador and D. S. Weld. M ulti-level m odeling of populations. In Fourth International Workshop on Qualitative Physics, 1990. [4] W anda A ustin and Behrokh Khoshnevis. Q ualitative m odling using natural language: A n application in system dynamics. 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