Johan de Kleer

A qualitative physics based on confluences

Abstract A qualitative physics predicts and explains the behavior of mechanisms in qualitative terms. The goals for the qualitative physics are (1) to be far simpler than the classical physics and yet retain all the important distinctions (e.g., state, oscillation, gain, momentum) without invoking the mathematics of continuously varying quantities and differential equations, (2) to produce causal accounts of physical mechanisms that are easy to understand, and (3) to provide the foundations for commonsense models for the next generation of expert systems. This paper presents a fairly encompassing account of qualitative physics. First, we discuss the general subject of naive physics and some of its methodological considerations. Second, we present a framework for modeling the generic behavior of individual components of a device based on the notions of qualitative differential equations (confluences) and qualitative state. This requires developing a qualitative version of the calculus. The modeling primitives induce two kinds of behavior, intrastate and interstate, which are governed by different laws. Third, we present algorithms for determining the behavior of a composite device from the generic behavior of its components. Fourth, we examine a theory of explanation for these predictions based on logical proof. Fifth, we introduce causality as an ontological commitment for explaining how devices behave.

Characterizing diagnoses and systems

Abstract Most approaches to model-based diagnosis describe a diagnosis for a system as a set of failing components that explains the symptoms. In order to characterize the typically very large number of diagnoses, usually only the minimal such sets of failing components are represented. This method of characterizing all diagnoses is inadequate in general, in part because not every superset of the faulty components of a diagnosis necessarily provides a diagnosis. In this paper we analyze the concept of diagnosis in depth exploiting the notions of implicate/implicant and prime implicate/implicant. We use these notions to consider two alternative approaches for addressing the inadequacy of the concept of minimal diagnosis. First, we propose a new concept, that of kernel diagnosis, which is free of this problem with minimal diagnosis. This concept is useful to both the consistency and abductive views of diagnosis. Second, we consider restricting the axioms used to describe the system to ensure that the concept of minimal diagnosis is adequate.

How circuits work

Abstract This paper presents a theory of commonsense understanding of the behavior of electronic circuits. It is based on the intuitive qualitative reasoning electrical engineers use when they analyze circuits. This intuitive reasoning provides a great deal of important information about the operation of the circuit, which although qualitative in nature, describes important quantitative aspects of circuit functioning (feedback paths, stability, impedance and gain estimates, etc.). One aspect of the theory, causal analysis, describes how the behavior of the individual components can be combined to explain the behavior of composite systems. Another aspect of the theory, teleological analysis, describes how the notion that the system has a purpose can be used to structure and aid this causal analysis. The theory is implemented in a computer program, EQUAL, which, given a circuit topology, can construct by qualitative causal analysis a description of the mechanism by which the circuit operates. This mechanism is then parsed by a grammar for circuit functions.

Problem solving with the ATMS

Abstract An assumption-based truth maintenance system provides a very general facility for all types of default reasoning. However, the ATMS is only one component of an overall reasoning system. This paper presents a set of concerns for interfacing with the ATMS, an interface protocol, and an example of a constraint language based on the protocol. The paper concludes with a comparison of the ATMS and the view of problem solving it entails with other approaches.

Extending the ATMS

Abstract The basic assumption-based truth maintenance (ATMS) architecture provides a foundation for implementing various kinds of default reasoning. This paper shows how the basic ATMS is extended to handle defaults and disjunctions of assumptions. These extensions are used to encode disjunctions of nodes, nonmonotonic justifications, normal defaults, nonnormal defaults, and arbitrary propositional formulas.

Using crude probability estimates to guide diagnosis

Abstract In order to identify the faulty components of a malfunctioning device in the fewest number of measurements, model-based diagnosis often uses a minimum entropy technique to select the next best measurement. This technique seems critically dependent on the availability of failure probabilities for components. Unfortunately, in many cases this information is unavailable or unknown. However, if we can assume that all components fail independently with equal probability and that components fail with very small probability, then it is possible to exploit the intuitions of the technique even when the exact probabilities are unknown. In addition, the computation required is much simpler. This approach can be generalized if the set of components can be partitioned such that each of the components of a partition fail with equal probability but are much more or less likely to fail than those of other partitions.

Qualitative reasoning with higher-order derivatives

The goals of qualitative physics are to identify the distinctions and laws which govern qualitative behavior of devices such that it is possible to predict and explain the behavior of physical devices without recourse to quantitative methods. Although qualitative analysis lacks quantitative information, it predicts significant characteristics of device functioning such as feedback, ringing, oscillation, etc. This paper defines higher-order qualitative derivatives and uses them to formulate six fundamental laws which govern the gross-time behavior of physical devices. These qualitative laws are based on the Mean Value Theorem and Taylors Expansion of the quantitative calculus. They substitute for what often requires sophisticated problem-solving. We claim they are the best that can be achieved relying on qualitative information.

Eliminating the Fixed Predicates from a Circumscription

Abstract Parallel predicate circumscription is the primary circumscriptive technique used in formalizing commonsense reasoning. In this paper we present a direct syntactic construction for transforming any parallel predicate circumscription using fixed predicates into an equivalent one which does not. Thus, we show that predicate circumscription is no more expressive with fixed predicates than without. We extend this result to prioritized circumscription. These results are expected to be useful for comparing circumscription to other nonmonotonic formalisms (such as autoepistemic logic and assumption-based truth maintenance) and for implementing fixed predicates.

Model-based computing for design and control of reconfigurable systems

Complex electro-mechanical products, such as high-end printers and photocopiers, are designed as families, with reusable modules put together in different manufacturable configurations, and the ability to add new modules in the field. The modules are controlled locally by software that must take into account the entire configuration. This poses two problems for the manufacturer. The first is how to make the overall control architecture adapt to, and use productively, the inclusion of particular modules. The second is to decide, at design time, whether a proposed module is a worthwhile addition to the system: will the resulting system perform enough better to outweigh the costs of including the module? This article indicates how the use of qualitative, constraint-based models provides support for solving both of these problems. This has become an accepted part of the practice of Xerox, and the control software is deployed in high-end Xerox printers.

Massively parallel assumption-based truth maintenance

De Kleers Assumption-based Truth Maintenance System (ATMS) is a propositional inference engine designed to simplify the construction of problem solvers that search complex search spaces efficiently. The ATMS has become a key component of many problem solvers, and often the primary consumer of computational resources. Although considerable effort has gone into designing and optimizing the LISP implementation, it now appears to be approaching the performance limitations of serial architectures. In this paper we show how the combination of a conventional serial machine and a massively parallel processor can dramatically speed up the ATMS algorithms, providing a very powerful general purpose architecture for problem solving.