Abstract: Once viewed as a rhetorical and superficial language phenomenon, metaphor is now recognized to serve a fundamental role in our conceptual structuring and language comprehension processes. In particular, it is argued that certain experiential metaphors based upon intuitions of spatial relations are inherent in the conceptual organization of our most abstract thoughts. In this paper we present a two-stage computational model of metaphor interpretation which employs a spatially founded semantics to broadly characterize the meaning carried by a metaphor in terms of a conceptual scaffolding, an interim meaning structure around which a fuller interpretation is fleshed out over time. We then present a semantics for the construction of conceptual scaffolding which is based upon core metaphors of collocation, containment and orientation. The goal of this scaffolding is to maintain the intended association of ideas even in contexts in which system knowledge is insufficient for a complete interpretation. This two-stage system of scaffolding and elaboration also models the common time lapse between initial metaphor comprehension and full metaphor appreciation. Several mechanisms for deriving elaborative inference from scaffolding structures, particularly in cases of novel or creative metaphor, are also presented. While the system developed in this paper has significant practical application, it also demonstrates that core spatial metaphors clearly play a central role in metaphor comprehension.

Abstract: In this paper, I present an architecture for generating extended text. This architecture is implemented in a system, Salix, which incrementally generates natural language texts whose structure is derived from the domain structure of the subject matter. The architecture is composed of data-driven, domain-independent strategies for producing increments of text. The strategies include metastrategies that combine or choose among all strategies that are applicable at each increment or decide what to do if no strategy applies. Salix's capabilities are demonstrated in generating texts, in the domains of houses and families, that are comparable to descriptions elicited from human speakers. Salix has also been utilized to generate texts about text style (Germain 1991). The approach to text generation presented here is compared to others in the literature along the dimensions of local organization, coherence, focusing, and domain independence. An argument is made for the approach presented here that locally organizes and incrementally generates coherent text.

Abstract: There have been many proposals for adding sound implementations of numeric processing to Prolog. This paper describes an approach to numeric constraint processing which has been implemented in Echidna, a new constraint logic programming (CLP) language. Echidna uses consistency algorithms which can actively process a wider variety of numeric constraints than most other CLP systems, including constraints containing some common nonlinear functions. A unique feature of Echidna is that it implements domains for real-valued variables with hierarchical data structures and exploits this structure using a hierarchical arc consistency algorithm specialized for numeric constraints. This gives Echidna two advantages over other systems. First, the union of disjoint intervals can be represented directly. Other approaches require trying each disjoint interval in turn during backtrack search. Second, the hierarchical structure facilitates varying the precision of constraint processing. Consequently, it is possible to implement more effective constraint processing control algorithms which avoid unnecessary detailed domain analysis. These advantages distinguish Echidna from other CLP systems for numeric constraint processing.

Abstract: A formal description is given of a connectionist implementation of discrete relaxation for labelled graph matching. The network is shown to converge. The desired behavior of the algorithm is formally specified; then it is proved that the result of the relaxation meets the formal goal. The network is limited by complexity considerations to the detection and propagation of unary and binary consistency constraints. The application is fast parallel indexing into a memory of object models, based on a visually derived junction/link structure description. Implementation experiments are presented, and explicit and exact space and time requirements are developed.

Abstract: We evaluate the success of the qualitative physics enterprise in automating expert reasoning about physical systems. The field has agreed, in essentials, upon a modeling language for dynamical systems, a representation for behavior, and an analysis method. The modeling language consists of generalized ordinary differential equations containing unspecified constants and monotonic functions; the behavioral representation decomposes the state space described by the equations into discrete cells; and the analysis method traces the transitory response using sign arithmetic and calculus. The field has developed several reasoners based on these choices over some 15 years. We demonstrate that these reasoners exhibit severe limitations in comparison with experts and can analyze only a handful of simple systems. We trace the limitations to inappropriate assumptions about expert needs and methods. Experts ordinarily seek to determine asymptotic behavior rather than transient response, and use extensive mathematical knowledge and numerical analysis to derive this information. Standard mathematics provides complete qualitative understanding of many systems, including those addressed so far in qualitative physics. Preliminary evidence suggests that expert knowledge and reasoning methods can be automated directly, without restriction to the accepted language, representation, and algorithm. We conclude that expert knowledge and methods provide the most promising basis for automating qualitative reasoning about physical systems.

Abstract: This special issue on the future of qualitative physics (QP) is exciting reading, filled with controversy. The issue starts with a position paper by Elisha Sacks and Jon Doyle which strongly criticizes aspects of the field; subsequent responses take a dizzying array of positions, many praising qualitative physics. In this introduction, I attempt to make sense of the debate. However, before summarizing the arguments, I briefly describe the field and its aspirations.

Abstract: Evidence from real discourse suggests that beliefs and other mental states (propositional attitudes) are often viewed by speakers and other agents in a metaphorical way. Typical metaphors are MIND-AS-CONTAINER—the view of the mind as a container, with thoughts being physical objects inside it—or IDEAS-AS-INTERNAL-UTTERANCES—the view of thoughts as natural language utterances inside an agent's head. It is therefore necessary for AI systems for mental-state representation/reasoning to reason within such views. This approach contrasts with the highly abstract logical stance adopted in most propositional attitude research. A formal representation scheme based on the various metaphors has been partially developed. In this paper, it is mainly the MIND-AS-CONTAINER segment of the formal representation scheme that is detailed. Inference processes operating over the scheme are also presented. The crucial distinguishing feature of the representation scheme is that the description of mental states is directly based on physical predicates, objects and so on, as opposed to abstract, tailor-made, mental ones. That is, the representation scheme is itself explicitly metaphor-imbued.

Abstract: Theories and computational models of metaphor comprehension generally circumvent the question of metaphor versus “anomaly” in favor of a treatment of metaphor versus literal language. Making the distinction between metaphoric and “anomalous” expressions is subject to wide variation in judgment, yet humans agree that some potentially metaphoric expressions are much more comprehensible than others. In the context of a program which interprets simple isolated sentences that are potential instances of cross-modal and other verbal metaphor, I consider some possible coherence criteria which must be satisfied for an expression to be “conceivable” metaphorically. Metaphoric constraints on object nominals are represented as abstracted or extended along with the invariant structural components of the verb meaning in a metaphor. This approach distinguishes what is preserved in metaphoric extension from that which is “violated”, thus referring to both “similarity” and “dissimilarity” views of metaphor. The role and potential limits of represented abstracted properties and constraints is discussed as they relate to the recognition of incoherent semantic combinations and the rejection or adjustment of metaphoric interpretations.

Abstract: Much research in machine learning has been focused on the problem of symbol-level learning (SLL), or learning to improve the performance of a program given examples of its behavior on typical inputs. A common approach to symbol-level learning is to use some sort of mechanism for saving and later reusing the solution paths used to solve previous search problems. Examples of such mechanisms are macro-operator learning, explanation-based learning, and chunking. However, experimental evidence that these mechanisms actually improve performance is inconclusive. This paper presents a formal framework for analysis of symbol-level learning programs, and then uses this framework to investigate a series of solution-path caching mechanisms which provably improve performance. The analysis of these mechanisms is illuminating in many respects; in particular, in order to obtain positive results, it is necessary to use a novel representation for a set of solution paths, and also to apply certain unusual optimizations to a set of solution paths. Several of the predictions made by the model have been confirmed by recently published experiments.

Abstract: There are two pertinent themes in the study of idioms in the area of natural language processing. Firstly, idioms should be defined and located in the space of non-literal expressions. This will be the first aim of this paper. Secondly, a processing model should be developed. In this paper, the application of knowledge representation techniques in three different models for the representation and processing of idioms are discussed. The first, a symbolic procedural model extends the two-level model which was originally developed in computational morphology. The second is a simple localist connectionist model. The third, a symbolic hierarchical model, represents idioms as part of a lexicon conceived as an inheritance hierarchy. A comparison between the models is made in which the focus lies on the resolution of the ambiguity of idioms, the relation between the literal and non-literal interpretation and the syntactic flexibility of idiomatic expressions.

Abstract: Based on psychological studies which show that metaphors and other non-literal constructions are comprehended in the same amount of time as comparable literal constructions, some researchers have concluded that literal meaning is not computed during comprehension of non-literal constructions. In this paper, we suggest that the empirical evidence does not rule out the possibility that literal meaning is constructed. We present a computational model of comprehension of non-literal expressions which is consistent with the data, but in which literal meaning is computed. This model has been implemented as part of a unification-based natural language processing system, called LINK.

Abstract: This article proposes a framework in which knowledge compilation can be exploited in a principled manner for the task of generating natural language. We have constructed an utterance generator for one side of a realistic dialogue that exploits compiled knowledge of, for instance, the effects of discourse pragmatics on text plans, and the effects of register, style, and politeness on text realization. The motivation for this work is the significant impact that compiled knowledge has on the speed of language generation.

Abstract: ions and generalization rules. For example, a human might be able to use the knowledge that reaching the same state again and again means that the system is in a cyclic state, and may make the inferential jump, even without advanced mathematical knowledge about dynamical systems. The QP calculi seem to have been designed under some implicit constraints, namely, that they display some of the perceived properties of human reasoning about the physical world: that humans often appear to combine causal relations recursively, and in cases where they have the structure of the physical system available, trace the topology of the physical system to follow the “flow of causality.” I will argue that QP techniques should aim to use the heuristic power of human reasoning even more, while employing the power of formal analysis to clearly defined subproblems where such techniques are needed. Thus, the issue is broadened to include: What should the connection of QP research be to human commonsense knowledge and reasoning about the physical world? Is Newtonian physical modeling sufficient for QP, or necessary for all the goals of QP? If one were only interested in producing a technology that assists in reasoning about the physical world, can one develop this technology without to some degree being concerned with human commonsense knowledge and reasoning methods? My concern is to ensure that qualitative physics 218 COMPUTATIONAL INTELLIGENCE research has a significant place not only for mathematically sophisticated analysis techniques as S&D propose, but also for a whole spectrum of issues concerning the sources of the power in human reasoning about the physical world. 3. HUMAN QUALITATIVE REASOMNG ABOUT THE PHYSICAL WORLD A trained physicist and an unschooled man-on-the-street start with a common ontology and a shared cognitive architecture. The physicist learns, and may add to, a specialized ontology as well, and acquires a number of modeling and analytical techniques. We need to sort out these distinct types of knowledge about the physical world that come into play in human reasoning. 1 . A commonsense ontology which predates and is in fact used by modem science: space, time, flow, physical objects, cause, state, perceptual primitives such as shapes, and so on. The commonsense ontology also comes with some terms that are given specific technical meanings by science, but in general the terms in this ontology are experientially and logically so fundamental that scientific theories are built on the infrastructure of this ontology. Early work in QP had as a main goal elaboration of such an ontology (Hayes 1979 and Forbus 1984 are examples). Even today, a good deal of QP research grapples with the development of ontologies for different parts of commonsense physical knowledge. 2. The scientific ontology is built on the commonsense ontology (and often gives specific technical meanings to some of the terms in it, such as “force”). Additional concepts and terms are constructed. Some of these are quite outside commonsense experience (examples are “voltage,” “current,” and “charm of quarks”). 3. Compiled causal knowledge. People compile causal expectations partly from direct experience and partly by caching some results from earlier problem solving. Which causal expectations get stored and used is largely determined by the relevance of the causes and effects to the goals of the problem solver. There is a more organized form of causal knowledge that we build up as well: models of causal processes. By process model I mean a description in terms of temporally evolving state transitions, where the state descriptions are couched using the commonsense and scientific ontologies. For example, we have commonsense causal processes such as “boiling,” or specialized ones such as “voltage amplification,” “the business cycle,” and so on. These are not neutral, agent-independent, process descriptions, but ones in which the qualitative states that participate in the description have been chosen based on abstractions of interest to the agent. In particular, such descriptions are couched in terms of possible intervention options on the world to affect the causal process, or observations to detect the process. Forbus’ processes (1984) and me and my colleagues’ work on functional representations (Sembugamoorthy and Chandrasekaran 1988; Goel 1989; Keuneke 1991 ; Sticklen and Tufankji 1991) are examples concerned with the development of representations for causal processes. When the process model is based on prescientific or unscientific views, we have naive process models (such as models of sun rotating around the earth, or of exorcism of evil spirits). Many prescientific process models are not only quite adequate, but are actually simpler and more computationally efficient than the scientific ones, for everyday purposes. These process descriptions are great organizing aids: they focus the direction of prediction, help in the identification of structures to realize desired functions in design (Goel 1989), and suggest actions to enable or abort the process. QP IS MORE THAN SPQR AND DYNAMICAL SYSTEMS THEORY 219 4. Mathematical equations embodying scientific laws and expressing relations between state variables. These equations themselves are acausal, and any causal direction is given by additional knowledge about which variables are exogenous. 4. SOME OF THE THINGS THAT A NEW QP SHOULD INCLUDE It is generally agreed, including by S&D, that a QP theory or framework should provide support for three components of reasoning about the physical world: modeling, prediction and control. In fact, a weakness of their paper is that they pay only lip service to the problem of modeling and fail to show why or how dynamic analysis will help solve that and the control problems. With the recent exception of SPQR calculi, quite a bit of the work in QP research is concerned with the development of ontologies, which are directly relevant to the modeling problem. Since I expect other respondents to outline precisely how the QP field is paying attention to these problems, I will concentrate on those aspects of the problem unlikely to be emphasized by them.

Abstract: PAU is an all-paths chart-based unification parser that uses the same uniform representation for regular syntax, irregular syntax such as idioms, and semantics PAU's representation has very little redundancy, simplifying the task of adding new semantics and syntax fo PAU's knowledge base PAU uses relations between the syntax and semantics to avoid the proliferation of rules found in semantic grammars By encoding semantics at the same level of representation as syntax, PAU is able to use semantic constraints early in the parse to eliminate semantically anomalous syntactic interpretations Examples are given to show how PAU can handle the many eccentricities of different idioms using the same mechanisms as are used to handle regular syntax and semantics These include the ability of some idioms, but not other idioms of the same syntactic form to undergo passivization, particle movement, action nominalization, indirect object movement, modification by adjectives, gerundive nominalization, prepositional phrase preposing, and topicalization PAU's representation is bidirectional and is also used by a companion generator PAU is designed to be efficient, runs in real time on typical workstations, and is being used in a number of natural language systems

Abstract: Sacks & Doyle provide an excellent overview of the fundamental limitations of the SPQR representations for reasoning about the qualitative properties of dynamic systems. We take this opportunity to outline some new directions for qualitative reasoning. In this paper, we provide a rigorous mathematical characterization for the term “qualitative property” in the context of static and dynamic systems. Based on these characterizations, we show that interval representations are well suited for reasoning about the qualitative properties of static systems such as qualitative comparative statics and qualitative stability. Moreover, we also show that symbolic computations help in the derivation of useful global properties of dynamic systems which can be used to guide numerical sampling of differential equations. The integration of symbolic and numeric methods provides a powerful approach for automating the qualitative analysis of differential equations.

Abstract: Non-literal language is also known as figurative language, or tropical language, and includes those devices (or tropes) whose meaning cannot be obtained by direct composition of their constituent words: idiom, metaphor, metonymy, simile, hyperbole, irony, sarcasm, indirect speech acts and implicature, among others. Non-literal language has historically been given scant attention as a research topic in the field of natural language processing (NLP), yet paradoxically, the ubiquity of nonliteral language is also cited as a major stumbling block to truly effective NLP. However, in recent years a community of researchers studying these phenomena has been growing and organizing. This growth led to a successful workshop on computational approaches to non-literal language held at the 12th IJCAI in Sydney, Australia in August 1992 (Fass et a f . 1991). This special issue grew out of that workshop and contains articles by some of the workshop participants plus others.

Abstract: Sacks and Doyle’s prolegomena is very narrowly focused on criticism of one particular class of techniques, which they call SPQR, for analyzing the behavior of a mathematical model. I cannot disagree with their statement of the limitations of SPQR and their call for the use of a wider range of more sophisticated mathematical techniques to analyze the behavior of dynamic systems. Nevertheless, I find it hard to hail their paper as a true prologue to future qualitative physics (QP) research for several reasons. For one, as evidenced by the number of papers analyzing the mathematical properties of SPQR and suggesting improvements (Raiman 1986, Kuipers 1987, Struss 1988), the field as a whole has long been aware of its limitations. Also, there have been a number of reports on different qualitative techniques for analyzing a model (Bhasker and Nigam 1990, Ishida 1989, Nishida et af. 1991, Sacks 1990). As someone who has tried to put qualitative reasoning in the context of more traditional mathematics (Kalagnanam et al. 1991), I do not see SPQR as the sole agreed-upon basis for qualitative physics research. More significantly, however, their prolegomena ignores several issues that I consider essential in QP research, reducing QP to automated mathematics. Important development in QP research has included ways to codify knowledge about the physical world besides techniques to use the knowledge to analyze behaviors (Forbus et af. 1980, 1984; Hayes 1985; Addanki 1989). QP researchers have also been concerned about how these reasoning methods relate to human commonsense reasoning. Compared to these aspects, the particular technique for analyzing mathematical models they chose to criticize is but a minor part of the whole QP endeavor. It is certainly true that SPQR is limited, and that we need to use more sophisticated mathematical techniques for analyzing models if accurate analysis is the goal. However, for each new analysis technique added to our bag of tricks, equally important issues are, What is the knowledge necessary to use the technique? How can it be encoded? and, above all, How does it contribute to the way people understand the physical world. A call for more sophisticated automated mathematical tools for analyzing physical situations in isolation from all these other issues would be like a call to build a more powerful calculator. Calculators have helped engineers solve engineering problems faster, and better ones will undoubtedly help even more. But, calculators have not taught us anything about the way we understand physical situations or suggested a way to codify knowledge underlying mathematical models. Sacks and Doyle do acknowledge that there are two different goals in QP, namely automating commonsense physical reasoning and automating expert reasoning. However, they dismiss the first goal as “controversial” and focus on the latter. In disagreement with Sacks and Doyle, I consider commonsense and causal reasoning as one of the essential aspects of QP that distinguishes it from automated mathematics or software engineering to build useful analysis tools. I include in “commonsense” reasoning an informed person’s reasoning about a complicated system at a level where detailed mathematical information is abstracted away. I also do not equate expertise with mathematical sophistication as Sacks and Doyle do. Some examples of commonsense reasoning: I-a person on the street-can reason about the consequences to a car engine running out of oil or coolant

Abstract: Looking to the future, generators will have more knowledge of language and will have to deal with inputs that are very rich in information. As a result, several problems will become more acute, including selecting what to say at the subproposition level and dealing with interaction among goals and dependencies among choices. This paper explains how these problems arise and why they are hard to handle within traditional architectures for generation. It also discusses why these issues have not been well addressed, including the current lack of demanding applications, excessive emphasis on linguistic traditions, the use of reverse engineering to determine generator inputs, and the tendency to research only one issue at a time.

Abstract: From my perspective as a mechanical designer and developer of theory and computation tools for mechanical design, Sacks and Doyle have provided a convincing and overdue challenge to qualitative simulation. SPQR is interesting, but involves a reduction from the expressive power of differential equations. Engineers generally need more rather than less expressive power; I am unaware of any successful applications of qualitative simulation in mechanical design. “Prolegomena . . .” explains why in clear and wellsupported terms. Sacks and Doyle rightly restrict themselves to conclusions for which they have evidence; having been asked for my opinion, I feel no such constraint. The following sections argue that Sacks and Doyle are in three ways too conservative. First, they seek only to reform qualitative physics, but no purely qualitative automated physics can be of much value to mechanical designers. Second, they underestimate the extent to which computational capabilities are a potential source of new mathematics. Finally, they do not go far enough in calling for a fusion between A1 and non-A1 fields.

Abstract: People use both expert and commonsense knowledge to reason about the behavior of physical systems in spite of incomplete knowledge. Problem-solving tasks such as diagnosis and design necessarily involve reasoning about systems which are incompletely known, but for which reliable behavioral predictions are important. A number of fields-ranging from economics, to the mathematics of dynamical systems, to artificial intelligence-have developed methods for determining the qualitative behavior of incompletely specified systems. Elisha Sacks and Jon Doyle (1992) (S+D) have written a critique of A1 research on qualitative reasoning, in which one useful contrast between research approaches is buried in a forest of misleading or incorrect claims. The useful contrast is between two reasonable approaches to exploring the space of models consistent with incomplete knowledge about a physical mechanism:

Abstract: 1 . Research on qualitative reasoning has not fulfilled its claims and not achieved its goal of successfully automating reasoning about a sufficiently broad class of physical systems. 2 . The reason €or (1) is that its current mainstream (called SPQR by the authors) is too limited and cannot overcome the limitations by simple extensions. 3. The essential limitation of the SPQR approach is that it focuses on transient behavior, whereas experts analyze asymptotic behavior. 4. The way out for qualitative reasoning is to concentrate on modeling experts’ use of sophisticated mathematical methods. 5 . The sophisticated mathematical models are essentially a. the qualitative theory of dynamic systems and b. numerical analysis.

Abstract: Sacks and Doyle (1992) point out the absence of mathematics from SPQR (simulation of processes by qualitative reasoning). Undoubtedly QR (qualitative reasoning) at large should embody knowledge about linearity, dynamical systems theory, and numerical analysis. There already exists software, in the form of numerical algorithms written mostly in C or FORTRAN, automating mathematical techniques; and software which acts as an intelligent coordinating interface among numerical modules, as well as between a user and the numerical modules (e.g., Konar et al. 1990), is a step further in this direction. What is not automated is the formulation of real scientific and engineering problems in a solvable mathematical form; i.e., the reasoning of the expert scientists or engineers who are users of existing sophisticated mathematical software. Expert reasoning requires skills which are still informal in the experts’ minds and need to be addressed by QR. These are largely domainand task-specific skills; while some unifying formalisms will undoubtedly emerge, we may be better off looking for them only after we tackle several specific subdomains. Automated construction of models is one of the important issues, and there has been a lot of quiet work in that direction (e.g., Stephanopoulos et al. 1987). Experts formulate, analyze, and revise specific equations (Sacks and Doyle 1992); what QR and A1 should focus on is not the mathematical side of using equations but the model construction and revision process which uses (a) information about the physical system; (b) the structure and results of previously tried models, analyzed and compared; and (c) information about the ultimate applicarion of the model which determines the goals of the modeling effort, because expert assumptions and simplifications are always context dependent. The context dependence of modeling is one of the most important characteristics of expert reasoning. It has not been addressed by SPQR, but it also receives little attention in Sacks and Doyle (1992). The expert makes just the right assumptions, drops what is unimportant or negligible in each particular portion of the model and for the particular system and task at hand, and comes up with a model ofjust the right complexity. The models and values we use in practice are never accurate. Variables never assume an exact value and they never become exactly equal to each other. To use the -, 0, and + values of SPQR, we have to decide how small a value is considered qualitatively zero, and we similarly have to determine when two values are considered equal. Order-ofmagnitude reasoning systems, such as O[M] (Mavrovouniotis and Stephanopoulos 1987, 1988; Mavrovouniotis et al. 1989), FOG (Raiman 1986; Dague et al. 1987), and other systems (Dubois and Prade 1989), aimed to address, in part, the issue of distinguishing between negligible and important parameters. These systems focused on relationships between parameters (which is a better approach than direct reference to “small” and “large” values), but they did not address the context dependence of order-of-magnitude arguments. Simply put, OEM] and FOG have no notion that the premise “ X i s approximately .

Abstract: Sacks and Doyle in their “Prolegomena” claim to “evaluate the success of the qualitative physics enterprise in automating expert reasoning about physical systems.” They present their view of the field, complain that this approach is inadequate, and suggest that an alternate approach would be better. Unfortunately, each part of their paper is either incorrect, misguided, or both. That is, (1) their view of qualitative physics, “simulation of processes by qualitative reasoning” (SPQR), is inaccurate and misleading, and (2) their account of expertise is wrong. This essay first argues that the aims and progress of qualitative physics, as described in the literature, differ substantially from Sacks and Doyle’s description, and second, that a close examination of how experts work suggests that the ideas and techniques developed in the last 15 years in qualitative physics will play a central role in making computers approach the depth and flexibility of expert reasoning about physical systems. Some of the suggestions phrased by Sacks and Doyle as a radical break from current practice are actually part of the way work in the field goes-hence the title of this essay.

Abstract: In their paper, ”Prolegomena to Any Future Qualitative Physics,” Elisha Sacks and Jon Doyle raise interesting points regarding the applicability of qualitative reasoning to solving practical engineering problems. They criticize in particular a line of research which they identify by the letters SPQR: the qualitative simulation of processes described by a set of differential equations. While many of their criticisms are interesting, the underlying assumption that all physical systems can be adequately represented by systems of equations is invalid. Engineering has no doubt benefited strongly from using mathematical concepts such as differential equations and dynamical systems theory. However, an engineer who wants to apply these concepts first has to construct a model where their use is tractable. Consider as an example the design and analysis of mechanisms such as clockworks. An important mechanism is the ratchet shown in Figure 1, a device which allows rotation of the wheel in one direction only. The literature gives many techniques for expressing the kinematic constraints of mechanisms as a system of equations. However, these techniques do not apply to the analysis of a ratchet mechanism. First, the kinematic constraints in a ratchet prohibit the parts from overlapping, but not from separating. They are nonholonomic ( [NIK88]) constraints, expressed as inequalities rather than equalities. Systems of inequalities by themselves generally do not give the unique solutions required for numerical methods. Thus,

Abstract: Sacks’ and Doyle’s “Prolegomena” is entirely convincing. If anyone thinks that the current generation of qualitative physics systems can analyze differential equations as well as an expert equipped with years of training in theoretical and numerical analysis, with the huge library of mathematical techniques developed over the last three centuries, and with good judgment on such matters as when to use which techniques, how far to trust a numerical simulation, and so on, deriving from a combination of experience, formal mathematical knowledge, and intuition, then they should certainly read this paper. They should also have their heads examined. Not since I last read Weizenbaum have I seen A1 research put down by a comparison to such an impossibly high standard, nor such a thoroughly straw man put up. No one in their right minds believes or ever believed that SPQR “obviate[s] other mathematical and scientific reasoning.” Nor has anyone ever claimed that SPQR “represents a monumental advance in mathematics,” or that “most expert reasoning involves only a few elements of calculus and interval arithmetic.” The fact that “experts far outperform SPQR” is no more an embarrassment to the state of A1 research than the fact that Shakespeare outperforms current natural language generators. Sacks and Doyle criticize SPQR for “lack[ing] any examples where experts draw incorrect . . . conclusions . . . while SPQR does better.” But this is a ridiculous standard, if only because the SPQR community claims that experts do (internally and largely unconsciously) carry out qualitative reasoning before proceeding with more detailed calculations. What is more to the point is that SPQR can sometimes detect errors in the blind use of other techniques. For example, a numerical simulation of the equation X = -2tx x3,x(0) = 1 that uses the simple linear extrapolation x(t + At) = x(t) + i ( t ) A t will, for any fixed value of At , predict that x eventually becomes negative. By contrast, SPQR applied to the confluence ax = [ t ] [x ] [x] predicts correctly that x never becomes negative. Of course, one can use a more sophisticated numerical technique, but guaranteeing that an algorithm using floating-point arithmetic will avoid this error is no trivial matter. And the numerical methods will be substantially more expensive computationally, and the conclusion that x remains positive will apply only to the interval computed, not to all positive t . SPQR has two major objectives. The first objective is to give a partial analysis of dynamic systems where only partial specifications are available. Complete information may be unobtainable for any of a number of reasons: you may not be able to perceive or acquire or compute the information, or the system may be an imaginary one that you are currently in the process of designing, or you may be reasoning generically about a large class of systems. In any of these cases, the known constraints may be very weak. If so, the techniques advocated by Sacks and Doyle are likely to be inapplicable, and the results that they are interested in, such as asymptotic stability, are likely to be undetermined. Still, there may be useful information to be extracted. The second objective of SPQR is to develop reasoning systems that are decomposable into a series of simple, local inferences, of such forms as “If X goes up, then Y will go up and 2 will go down,” and “Since X is a lot bigger than Y, 2 will be a lot bigger than W.” Necessarily, such restricted forms of inference are weak. However, the fact that the

Abstract: The starting point for this commentary is Sacks’ and Doyle's conclusion that a central problem for qualitative physics is automating mathematical model formulation. We believe that model formulation is also a central problem for operations research, and although we have focused on models for production planning rather than for engineering systems analysis, our experience confirms that of Sacks and Doyle, that at least parts of model formulation are amenable to automation. In terms of their recommendations for future research, their strategy seems to emphasize the formalization of mathematical knowledge. We wish to stress that understanding the design or analysis context, the problem domain, and resource constraints on the modeling process is equally important. Methods used in cognitive psychology for understanding human problem solving, such as protocol analysis, can complement mathematical study by helping us understanding the processing that human modelers use to bring mathematical knowledge to bear. We have been using the results of such analyses to guide the creation of a model formulation system (MFS) within the Soar architecture. The use of cognitive studies and computer models in tandem seems to represent a viable strategy for making progress in this area.

Abstract: One can respond to “Prolegomena to any Future Qualitative Physics” at several levels. As practitioners in the field, it is easy to become incensed and respond to every minute misrepresentation and error. This would unfortunately miss the forest for the trees. Unfortunate, because there is a much simpler story to be told here. Sacks and Doyle make two high-level claims as the basic theme of their paper. First, they state that the field of qualitative reasoning is roughly equivalent to SPQR. In other words, the principal goal of the qualitative reasoning enterprise is to (1) produce abstract state transition diagrams of system behavior (i.e., simulations) which are (2) solely for the purpose of predicting behavior. Second, in reasoning about such systems’ behavior, “experts” are predominantly concerned with their asymptotic, dynamical properties. As stated, we view both points as incorrect, misleading, and quite surprising coming from Sacks, who, as a frequent attendee of the qualitative reasoning workshops, should have a better understanding of the field. However, there is another, less controversial interpretation of the paper which we obtained from personal conversations with Sacks at the most recent workshop. First, their argument was intended to address work on the SPQR subset of the field rather than suggest that all of qualitative reasoning is SPQR. Second, their reference to the concerns of an expert was refemng to an expert academic dynamicist, and was a suggestion about how to compare the relative merits of SPQR and dynamical analysis. Given this interpretation shift, Sacks and Doyle’s paper raises an interesting, but much narrower, technical issue related to acausal simulation, a small portion of the work going on in the field of qualitative reasoning. One argument in favor of qualitative simulation (SPQR) is that qualitative differential equations enable reasoning about entire classes of functions and is thus a more efficient way to perform certain tasks, such as the preliminary stages of design. Alternatively, Sacks and Doyle argue that it is better to pick a specific differential equation, analyze its solutions using conventional techniques, and if these are undesirable (for the task, say diagnosis or design) to pick another one. We believe that neither has demonstrated clear superiority for the kinds of tasks qualitative simulation is intended to address and we think it is perfectly reasonable that researchers in qualitative simulation explore and evaluate both approaches. Rather than focus on that debate in our response, we instead address the broader issues that have arisen while discussing this paper. We try to clarify what we see as the goals of the field and describe some of the major research efforts.

Abstract: Sacks and Doyle have done the A1 community a service by spelling out the limitations of the qualitative physics/reasoning/simulation approach (SPQR). SPQR is one of those approaches that initially looked neat, but did not pan out in practice. Sacks and Doyle note that “. . . there are other simple and common systems that SPQR still cannot comprehend after IS years of investigation.” I believe these meager achievements are largely a result of an artificial distinction between qualitative and quantitative reasoning built into the SPQR approach. This distinction inhibits smooth mixing of qualitative to quantitative reasoning as needed. An alternative approach is to regard a qualitative prediction (e.g., pressure P1 will increase) as a weakly informative quantitative prediction, by representing our knowledge of P1 as a flat probability density between the minimum and maximum pressure. Such a representation says in effect that we know nothing about P1 other than that it is positive. Better knowledge about the value of P1 can be expressed as a peaked distribution around some mean value-the better the knowledge, the sharper the peak. Such a probabilistic representation allows reasoning at a level of detail appropriate to the problem at hand, and in effect claims that all system knowledge is quantitative to some degree. As Sacks and Doyle point out, an expert trying to design/diagnose/understand/controVmodeY . . . a complex system uses an intimate mixture of both qualitative and quantitative reasoning. However, instead of further SPQR bashing, I want to expand on the method of combining both quantitative and qualitative reasoning into a coherent whole, as a constructive extension of Sacks and Doyle’s critique. Attempts have been made to graft quantitative knowledge onto basically qualitative systems using ranges and inequalities (e.g., Simmons 1986; Kuipers and Berleant 1988). While this is clearly an improvement over purely qualitative approaches, it has a number of problems. For example, the all-or-nothing nature of a range means that a slight change in the range associated with say a pressure variable can lead to qualitatively different predictions (e.g., that a relief valve will open)-brittle behavior that is purely the result of using ranges and logical inference where it is not appropriate. In a smooth probabilistic representation of the same situation, a11 that changes is the probability that the relief valve will open. A desirable criterion for any system that represents and reasons about complex situations is that the system should be able to smoothly adjust the accuracy of its reasoning to one that is appropriate for answering the current question. Unfortunately, even SPQR augmented with ranges does not meet this criterion, because if the ranges are reduced to points (no uncertainty) the SPQR system is still doing range arithmetic, not numerical simulation. In other words, when uncertainty is added to a standard differential equation system model, SPQR requires an abrupt change in the type of inference performed. Much more serious is that the proposed inference procedures for these quantitative ranges can lead to erroneous conclusions. For any set of mutually constrained variables

Abstract: I am quite sympathetic to the views presented by Sacks and Doyle in “Prolegomena.” It is a provocative paper, but I hope qualitative reasoning researchers will respond actively to the challenges posed in “Prolegomena,” and not regard it as a personal attack. The paper contains a number of valid criticisms. Sacks and Doyle claim that the representation adopted by qualitative reasoning researchers is an inadequate representation for many reasoning problems, a claim with which I agree. To date, qualitative reasoning research has concentrated mainly on simple linear systems, and on an even smaller set of nonlinear systems. With success in those endeavors, the attitude now seems to be that the mathematics of qualitative reasoning is complete and well understood; the new challenge is that of automating model building and model management (Weld 1989; Crawford et af. 1990). Model building is indeed an important task. However, useful models can be built only if there is an adequate vocabulary to describe the concepts used in the model. Sacks and Doyle are quite right to point out that the mathematics of qualitative reasoning is neither complete nor well understood. The real world is a highly nonlinear place. The qualitative calculus adopted by most researchers is inadequate for representing and reasoning about large portions of real-world knowledge mainly because of nonlinearity. I will illustrate this point with an example from the domain of kinematics. The field of kinematics deals with the geometric relationships between different bodies, and with how these relationships constrain the relative motion of the bodies in space. Most work in this area has focused on “fixed-axis’’ mechanisms, which can be solved using relatively efficient algorithms. However, mechanical linkages, which include “moving-axis” mechanisms, display a wider range of complicated behaviors which cannot be handled adequately with current qualitative reasoning techniques. Take, for example, Kim’s work in the qualitative kinematic analysis of four-bar linkages (Kim 1990). Kim’s program can “simulate” four-bar linkages (the simplest possible linkages) at a qualitative level, distinguishing between behavioral classes (e.g., drag-link or crank-rocker) as a function of relative link lengths. This is interesting and useful. Yet to call this work a true success is rather misleading: Kim’s program can answer only a few of the questions a kinematics expert is likely to have when using a linkage in a particular design context. The interesting information in the majority of four-bar linkage designs is not the relative angles of the links-which is what Kim’s program computes-but rather the position and orientation of a point on the coupler link (the one connecting the two cranks). Some questions an engineer might have are: Does the coupler point trace a closed path in space? Does the path approximate a straight line (or perhaps a circular arc) for some fraction of its motion? What is the relationship of coupler curve shape (or the speed of traversal) to the lengths of the various links? How many times does the curve cross itself? The answers require specific reasoning about highly nonlinear systems, a task which SPQR systemsand Kim’s system-are incapable of performing. In short, SPQR can solve the “easy”-i.e., linear or simple nonlinear-problems in simulation and envisionment of a mechanical design. The more interesting, detailed ques-