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Qualitative reasoning about physical systems: An introduction
ARTIFICIAL INTELLIGENCE
1
Qualitative Reasoning about Physical Systems: An Introduction Daniel G. B o b r o w X E R O X Palo Alto Research Center, Palo Alto, CA 94304, U.S.A.
This volume brings together current work on qualitative reasoning. Previous publication has been primarily in scattered conference proceedings. The appearance of this volume reflects the maturity of qualitative reasoning as a research area, and the growing interest in problems of reasoning about physical systems. The papers present knowledge bases for a number of very different domains, from heat flow, to transistors, to digital computation. Anyone concerned with automated reasoning about the real (physical) world should read and understand this material.
Compositionality A common theme of all these papers is explaining how physical systems work. An important shared criterion is that the behavioral description must be compositional, that is the description of a system's behavior must be derivable from the structure of the system. The term 'structure' refers to the components of the analysis, component behaviors, and the connections between components. The term 'behavior' refers to the time course of observable changes of state of the components and the system as a whole. Each component has some associated behavior, and the behavior of the system as a whole results from the interactions of the behaviors of the components through specified connections.
Locality A shared criterion for explanation is that effects must propogate locally, through specified connections. Explanations which follow such local propagation rules are felt to be causal. This contrasts sharply with standard physics. In that paradigm, systems are described by differential equations which provide constraints on the dynamics of system state variables. Analytic techniques determine allowable time-varying behavior of these continuous state Artificial Intelligence 24 (1984) 1-5 0004-3702/84/$3.00 © 1984, Elsevier Science Publishers B.V. (North-Holland)
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variables, but there is no sense from these solutions of how that time course comes to be. Descriptive terms for behavior such as 'oscillatory' and ' d a m p e d ' are derived from examining the shapes of the resulting functions of time, rather than from an understanding of the causal processes which underly the system. (See the discussion in De Kleer and Brown on Physics.)
Function Designed artifacts have a function : the relation between a goal of a human user and the behavior of a system. Functionality is a different level of description than behavior. For example, the behavior of the hour hand of a clock can be described in terms of rotation around a point, whereas its function is to indicate the hour to an observer. The function of a piece of a system relates the behavior of that piece to the function of the system as a whole. Reasoning about function can facilitate understanding of system behavior. It may also allow interesting optimizations in system design. A completely different kind of structure may be substituted for a piece of a larger system if the two structures provide the same function; e.g., using a quartz crystal in a watch as a time standard instead of a balance wheel.
System Tasks The authors describe how systems can perform a n u m b e r of different qualitative reasoning tasks. We use this as a primary index into the papers in this volume, indicated by authors' names in parentheses. Simulation: Starting with a structural description of some device or system, and some initial conditions, determine a likely course of future behavior. When there is ambiguity in the possible behavior which cannot be resolved, ask the user or decide arbitrarily (Forbus, Kuipers, Williams). Envisionment: Starting with a structural description, determine all possible behavioral sequences (De Kleer, De Kleer and Brown). Two criteria must be met: all possible envisioned behaviors can be realized in some real system with some choice of parameters (realizability); and all possible real systems follow one of these behaviors (completeness). Mental models: People reason about system behavior in ways inconsistent with physically realizable systems. Sometimes their models may be realizable, but not causal. Capturing such reasoning processes (Forbus, Kuipers) requires models which don't satisfy all the criteria for a good qualitative physics model (see the discussions of De Kleer and Brown, De Kleer, Williams). Nonetheless, the language of qualitative reasoning, particularly encapsulated histories, provide ways of modeling this process. Diagnosis: A system is 'misbehaving' if its composed behavior (as computed from its assumed structure) is different than some specified desired behavior. For systems which previously behaved correctly, the problem is to find the change in the underlying structure which is causing the difference in behavior
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INTRODUCTION
(Davis, Genesereth). The problem is to limit the search for changes (since unlimited search can result in hypothesizing a completely new structure--an unlikely event). Verification: Designed systems start with a behavior specification to achieve a system function. Any number of structures may be used to try to implement such a specification. The problem of verification (Barrow) is to ascertain that a particular implementation structure has a composite behavior which matches the desired behavior specification. Deducing functionality: For people to understand explanations of complex devices, it is useful to identify the function of components in terms common to the field. Extracting functional descriptions from structural and behavioral descriptions can be done by examining the mechanism graph for an electric circuit (De Kleer).
Discrete versus Continuous Systems Another distinction among qualitative reasoners is whether the devices and processes they reason about have state variables that are inherently discrete (a relatively small number of values), or continuous (real-valued functions). The diagnosis and verification programs (Genesereth, Davis, Barrow) all deal with digital computation, and are discrete systems. The rest all do qualitative reasoning about continuous systems.
Quantity Spaces Qualitative reasoning about continuous domains requires quantization of the domain to a discrete symbol set. The values chosen reflect open regions of qualitatively uniform component behavior, and values at important boundaries where interesting transitions occur only at these boundary points. For example, with respect to a spring attached to a mass, the qualitative values of the force exerted by the spring can be mapped into three values for qualitative reasoning: positive (exerting force to the right, say), zero (at its rest length) or negative (exerting force to the left). Following Hayes' discussion in his Naive Physics Manifesto, a discrete representation of a continuous space is called a 'quantity space'. Forbus has an extended discussion of quantity spaces. The simple quantity space {+,0,-} illustrated above suffices for many devices described in these papers (e.g., De Kleer, De Kleer and Brown, Williams). Williams also shows how more complex quantity spaces can be usefully mapped into this simpler space.
Ontological Primitives There is another ontological choice to be made in a knowledge base for quantitative reasoning: what are the primitive elements of structural descriptions? Kuipers makes the jump from quantitative differential equations directly
4
D.G. BOBROW
to qualitative constraints among state variables of a system. The components are only state variables, and the connections are the constraints. His simulation assumes that causality is identical to value propagation with constraints. A device-centered ontology is used by D e Kleer, Brown and Williams. The primitives are devices such as pipes, valves and springs, or resistors, capacitors and transistors. Network laws provide constraints at connection points (e.g. that the total current into a point is zero). Brown and De Kleer take much care to ensure that their device models do not e m b e d unstated assumptions about the context in which these devices are placed. They have an important discussion of criteria for device-model selection for physics. The digital papers (Davis, Genesereth, Barrow) also use a device-centered ontology, but their choice of c o m p o n e n t models is much clearer since the devices are defined digitally. Forbus uses an ontology based on the concept of process as the medium for transfer of causality. A single process is described as affecting a number of individuals; this combination of effects is expressed more easily than in device-centered ontology. However, in the process-centered ontology, it is harder to be sure that one has specified all ways a system can affect an individual than it is in the device-centered ontology where connections determine effects. Forbus has extended Pat Hayes' notion of 'history' to allow easier modeling of people's naive reasoning. Forbus also has a very interesting discussion of how processes and histories define the AI 'frame problem' out of existence, replacing it with the new and hopefully more tractable problems of local evolution and intersection/interaction.
Implementation Most of the systems described here use propagation of constraints in their implementation. Of particular note is De Kleer's discussion of implementation problems, and his techniques for obtaining choices without backtracking. Davis uses successive suspension of constraints to control search for modifications to the structural descriptions to account for misbehavior. H e uses both physical and electrical descriptions of a single system. Davis's system 'discovers' a failure caused by a bent connector pin which effectively added a wire to the system. Thus this short between two points changed the topology of the circuit. However, by using possible close 'pathways of interactions' this was discovered without having to examine very many possible circuit changes. Barrow and G e n e s e r e t h both use logic-based reasoners. Barrow uses PROLO(~, and extends the proof procedures e m b e d d e d in PROLO6 to do case enumeration when appropriate, and unrolling of sequential behavior. Genesereth has extended the notion of resolution to use resolution residue to guide search in his diagnosis program.
INTRODUCTION
5
Notation The planning for this volume caused some convergence in the research, as can be seen in the occurrence of similar ideas in several papers. It also caused some convergence in the notation used by the authors, though not nearly enough for my taste. Williams, De Kleer and Brown use a common notation for qualitative values. Forbus uses a different one which separates magnitudes of quantities and their signs. Kuipers shows how new points in the quantity space can arise from analysis of the behavior of the system. Full convergence awaits the grand synthesis of all these ideas, and the appearance of a widely accepted teaching text. ACKNOWLEDGMENT
I want to thank all of the authors, who in addition to writing and rewriting their own papers, contributed greatly to the quality and coherence of this volume by providing careful critiques of other papers. I am grateful to John Seely Brown who encouraged me to put together this special volume, to John and Johan De Kleer for seducing me into thinking about problems in qualitative reasoning, and to Mark Stefik for his aid and general support. Finally, I want to thank North-Holland for making a special effort to get this volume out in a timely manner, both in the AI Journal and as a book.
1
Qualitative Reasoning about Physical Systems: An Introduction Daniel G. B o b r o w X E R O X Palo Alto Research Center, Palo Alto, CA 94304, U.S.A.
This volume brings together current work on qualitative reasoning. Previous publication has been primarily in scattered conference proceedings. The appearance of this volume reflects the maturity of qualitative reasoning as a research area, and the growing interest in problems of reasoning about physical systems. The papers present knowledge bases for a number of very different domains, from heat flow, to transistors, to digital computation. Anyone concerned with automated reasoning about the real (physical) world should read and understand this material.
Compositionality A common theme of all these papers is explaining how physical systems work. An important shared criterion is that the behavioral description must be compositional, that is the description of a system's behavior must be derivable from the structure of the system. The term 'structure' refers to the components of the analysis, component behaviors, and the connections between components. The term 'behavior' refers to the time course of observable changes of state of the components and the system as a whole. Each component has some associated behavior, and the behavior of the system as a whole results from the interactions of the behaviors of the components through specified connections.
Locality A shared criterion for explanation is that effects must propogate locally, through specified connections. Explanations which follow such local propagation rules are felt to be causal. This contrasts sharply with standard physics. In that paradigm, systems are described by differential equations which provide constraints on the dynamics of system state variables. Analytic techniques determine allowable time-varying behavior of these continuous state Artificial Intelligence 24 (1984) 1-5 0004-3702/84/$3.00 © 1984, Elsevier Science Publishers B.V. (North-Holland)
2
D.G. BOBROW
variables, but there is no sense from these solutions of how that time course comes to be. Descriptive terms for behavior such as 'oscillatory' and ' d a m p e d ' are derived from examining the shapes of the resulting functions of time, rather than from an understanding of the causal processes which underly the system. (See the discussion in De Kleer and Brown on Physics.)
Function Designed artifacts have a function : the relation between a goal of a human user and the behavior of a system. Functionality is a different level of description than behavior. For example, the behavior of the hour hand of a clock can be described in terms of rotation around a point, whereas its function is to indicate the hour to an observer. The function of a piece of a system relates the behavior of that piece to the function of the system as a whole. Reasoning about function can facilitate understanding of system behavior. It may also allow interesting optimizations in system design. A completely different kind of structure may be substituted for a piece of a larger system if the two structures provide the same function; e.g., using a quartz crystal in a watch as a time standard instead of a balance wheel.
System Tasks The authors describe how systems can perform a n u m b e r of different qualitative reasoning tasks. We use this as a primary index into the papers in this volume, indicated by authors' names in parentheses. Simulation: Starting with a structural description of some device or system, and some initial conditions, determine a likely course of future behavior. When there is ambiguity in the possible behavior which cannot be resolved, ask the user or decide arbitrarily (Forbus, Kuipers, Williams). Envisionment: Starting with a structural description, determine all possible behavioral sequences (De Kleer, De Kleer and Brown). Two criteria must be met: all possible envisioned behaviors can be realized in some real system with some choice of parameters (realizability); and all possible real systems follow one of these behaviors (completeness). Mental models: People reason about system behavior in ways inconsistent with physically realizable systems. Sometimes their models may be realizable, but not causal. Capturing such reasoning processes (Forbus, Kuipers) requires models which don't satisfy all the criteria for a good qualitative physics model (see the discussions of De Kleer and Brown, De Kleer, Williams). Nonetheless, the language of qualitative reasoning, particularly encapsulated histories, provide ways of modeling this process. Diagnosis: A system is 'misbehaving' if its composed behavior (as computed from its assumed structure) is different than some specified desired behavior. For systems which previously behaved correctly, the problem is to find the change in the underlying structure which is causing the difference in behavior
3
INTRODUCTION
(Davis, Genesereth). The problem is to limit the search for changes (since unlimited search can result in hypothesizing a completely new structure--an unlikely event). Verification: Designed systems start with a behavior specification to achieve a system function. Any number of structures may be used to try to implement such a specification. The problem of verification (Barrow) is to ascertain that a particular implementation structure has a composite behavior which matches the desired behavior specification. Deducing functionality: For people to understand explanations of complex devices, it is useful to identify the function of components in terms common to the field. Extracting functional descriptions from structural and behavioral descriptions can be done by examining the mechanism graph for an electric circuit (De Kleer).
Discrete versus Continuous Systems Another distinction among qualitative reasoners is whether the devices and processes they reason about have state variables that are inherently discrete (a relatively small number of values), or continuous (real-valued functions). The diagnosis and verification programs (Genesereth, Davis, Barrow) all deal with digital computation, and are discrete systems. The rest all do qualitative reasoning about continuous systems.
Quantity Spaces Qualitative reasoning about continuous domains requires quantization of the domain to a discrete symbol set. The values chosen reflect open regions of qualitatively uniform component behavior, and values at important boundaries where interesting transitions occur only at these boundary points. For example, with respect to a spring attached to a mass, the qualitative values of the force exerted by the spring can be mapped into three values for qualitative reasoning: positive (exerting force to the right, say), zero (at its rest length) or negative (exerting force to the left). Following Hayes' discussion in his Naive Physics Manifesto, a discrete representation of a continuous space is called a 'quantity space'. Forbus has an extended discussion of quantity spaces. The simple quantity space {+,0,-} illustrated above suffices for many devices described in these papers (e.g., De Kleer, De Kleer and Brown, Williams). Williams also shows how more complex quantity spaces can be usefully mapped into this simpler space.
Ontological Primitives There is another ontological choice to be made in a knowledge base for quantitative reasoning: what are the primitive elements of structural descriptions? Kuipers makes the jump from quantitative differential equations directly
4
D.G. BOBROW
to qualitative constraints among state variables of a system. The components are only state variables, and the connections are the constraints. His simulation assumes that causality is identical to value propagation with constraints. A device-centered ontology is used by D e Kleer, Brown and Williams. The primitives are devices such as pipes, valves and springs, or resistors, capacitors and transistors. Network laws provide constraints at connection points (e.g. that the total current into a point is zero). Brown and De Kleer take much care to ensure that their device models do not e m b e d unstated assumptions about the context in which these devices are placed. They have an important discussion of criteria for device-model selection for physics. The digital papers (Davis, Genesereth, Barrow) also use a device-centered ontology, but their choice of c o m p o n e n t models is much clearer since the devices are defined digitally. Forbus uses an ontology based on the concept of process as the medium for transfer of causality. A single process is described as affecting a number of individuals; this combination of effects is expressed more easily than in device-centered ontology. However, in the process-centered ontology, it is harder to be sure that one has specified all ways a system can affect an individual than it is in the device-centered ontology where connections determine effects. Forbus has extended Pat Hayes' notion of 'history' to allow easier modeling of people's naive reasoning. Forbus also has a very interesting discussion of how processes and histories define the AI 'frame problem' out of existence, replacing it with the new and hopefully more tractable problems of local evolution and intersection/interaction.
Implementation Most of the systems described here use propagation of constraints in their implementation. Of particular note is De Kleer's discussion of implementation problems, and his techniques for obtaining choices without backtracking. Davis uses successive suspension of constraints to control search for modifications to the structural descriptions to account for misbehavior. H e uses both physical and electrical descriptions of a single system. Davis's system 'discovers' a failure caused by a bent connector pin which effectively added a wire to the system. Thus this short between two points changed the topology of the circuit. However, by using possible close 'pathways of interactions' this was discovered without having to examine very many possible circuit changes. Barrow and G e n e s e r e t h both use logic-based reasoners. Barrow uses PROLO(~, and extends the proof procedures e m b e d d e d in PROLO6 to do case enumeration when appropriate, and unrolling of sequential behavior. Genesereth has extended the notion of resolution to use resolution residue to guide search in his diagnosis program.
INTRODUCTION
5
Notation The planning for this volume caused some convergence in the research, as can be seen in the occurrence of similar ideas in several papers. It also caused some convergence in the notation used by the authors, though not nearly enough for my taste. Williams, De Kleer and Brown use a common notation for qualitative values. Forbus uses a different one which separates magnitudes of quantities and their signs. Kuipers shows how new points in the quantity space can arise from analysis of the behavior of the system. Full convergence awaits the grand synthesis of all these ideas, and the appearance of a widely accepted teaching text. ACKNOWLEDGMENT
I want to thank all of the authors, who in addition to writing and rewriting their own papers, contributed greatly to the quality and coherence of this volume by providing careful critiques of other papers. I am grateful to John Seely Brown who encouraged me to put together this special volume, to John and Johan De Kleer for seducing me into thinking about problems in qualitative reasoning, and to Mark Stefik for his aid and general support. Finally, I want to thank North-Holland for making a special effort to get this volume out in a timely manner, both in the AI Journal and as a book.