Jon Doyle

Non-monotonic logic I

Abstract ‘Non-monotonic’ logical systems are logics in which the introduction of new axioms can invalidate old theorems. Such logics are very important in modeling the beliefs of active processes which, acting in the presence of incomplete information, must make and subsequently revise assumptions in light of new observations. We present the motivation and history of such logics. We develop model and proof theories, a proof procedure, and applications for one non-monotonic logic. In particular, we prove the completeness of the non-monotonic predicate calculus and the decidability of the non-monotonic sentential calculus. We also discuss characteristic properties of this logic and its relationship to stronger logics, logics of incomplete information, and truth maintenance systems.

A truth maintenance system

Abstract To choose their actions, reasoning programs must be able to make assumptions and subsequently revise their beliefs when discoveries contradict these assumptions. The Truth Maintenance System (TMS) is a problem solver subsystem for performing these functions by recording and maintaining the reasons for program beliefs. Such recorded reasons are useful in constructing explanations of program actions and in guiding the course of action of a problem solver. This paper describes (1) the representations and structure of the tms , (2) the mechanisms used to revise the current set of beliefs, (3) how dependency-directed backtracking changes the current set of assumptions, (4) techniques for summarizing explanations of beliefs, (5) how to organize problem solvers into “dialectically arguing” modules, (6) how to revise models of the belief systems of others, and (7) methods for embedding control structures in patterns of assumptions. We stress the need of problem solvers to choose between alternative systems of beliefs, and outline a mechanism by which a problem solver can employ rules guiding choices of what to believe, what to want, and what to do.

Background to Qualitative Decision Theory

■ This article provides an overview of the field of qualitative decision theory: its motivating tasks and issues, its antecedents, and its prospects. Qualitative decision theory studies qualitative approaches to problems of decision making and their sound and effective reconciliation and integration with quantitative approaches. Although it inherits from a long tradition, the field offers a new focus on a number of important unanswered questions of common concern to AI, economics, law, psychology, and management.

Two theses of knowledge representation: language restrictions, taxonomic classification, and the utility of representation services

Abstract Levesque and Brachman argue that in order to provide timely and correct responses in the most critical applications, general-purpose knowledge representation systems should restrict their languages by omitting constructs which require nonpolynomial worst-case response times for sound and complete classification. They also separate terminological and assertional knowledge, and restrict classification to purely terminological information. We demonstrate that restricting the terminological language and classifier in these ways limits these “general-purpose” facilities so severely that they are no longer generally applicable. We argue that logical soundness, completeness, and worst-case complexity are inadequate measures for evaluating the utility of representation services, and that this evaluation should employ the broader notions of utility and rationality found in decision theory. We suggest that general-purpose representation services should provide fully expressive languages, classification over relevant contingent information, “approximate” forms of classification involving defaults, and rational management of inference tools.

Prospects for Preferences

This article examines prospects for theories and methods of preferences, both in the specific sense of the preferences of the ideal rational agents considered in economics and decision theory and in the broader interplay between reasoning and rationality considered in philosophy, psychology, and artificial intelligence. Modern applications seek to employ preferences as means for specifying, designing, and controlling rational behaviors as well as descriptive means for understanding behaviors. We seek to understand the nature and representation of preferences by examining the roles, origins, meaning, structure, evolution, and application of preferences.

Impediments to universal preference-based default theories

Research on nonmonotonic and default reasoning has identified several important criteria for preferring alternative default inferences. The theories of reasoning based on each of these criteria may uniformly be viewed as theories of rational inference, in which the reasoner selects maximally preferred states of belief. Though researchers have noted some cases of apparent conflict between the preferences supported by different theories, it has been hoped that these special theories of reasoning may be combined into a universal logic of nonmonotonic reasoning. We show that the different categories of preferences conflict more than has been realized, and adapt formal results from social choice theory to prove that every universal theory of default reasoning will violate at least one reasonable principle of rational reasoning. Our results can be interpreted as demonstrating that, within the preferential framework, we cannot expect much improvement on the rigid lexicographic priority mechanisms that have been proposed for conflict resolution.

A model for deliberation, action, and introspection

This thesis investigates the problem of controlling or directing the reasoning and actions of a computer program. The basic approach explored is to view reasoning as a species of action, so that a program might apply its reasoning powers to the task of deciding what inferences to make as well as to deciding what other actions to take. A design for the architecture of reasoning programs is proposed. This architecture involves self-consciousness, intentional actions, deliberate adaptations, and a form of decision-making based on dialectical argumentation. A program based on this architecture inspects itself, describes aspects of itself to itself, and uses this self-reference and these self-descriptions in making decisions and taking actions. The programs mental life includes awareness of its own concepts, beliefs, desires, intentions, inferences, actions, and skills. All of these are represented by self-descriptions in a single sort of language, so that the program has access to all of these aspects of itself, and can reason about them in the same terms.

Belief Revision: Reason maintenance and belief revision: Foundations versus coherence theories

Recent years have seen considerable work on two approaches to belief revision: the so-called foundations and coherence approaches. The foundations approach supposes that a rational agent derives its beliefs from justifications or reasons for these beliefs: in particular, that the agent holds some belief if and only if it possesses a satisfactory reason for that belief. According to the foundations approach, beliefs change as the agent adopts or abandons reasons. The coherence approach, in contrast, maintains that pedigrees do not matter for rational beliefs, but that the agent instead holds some belief just as long as it logically coheres with the agent’s other beliefs. More specifically, the coherence approach supposes that revisions conform to minimal change principles and conserve as many beliefs as possible as specific beliefs are added or removed. The artificial intelligence notion of reason maintenance system (Doyle, 1979) (also called “truth maintenance system”) has been viewed as exemplifying the foundations approach, as it explicitly computes sets of beliefs from sets of recorded reasons. The so-called AGM theory of Alchourrón, Gärdenfors and Makinson (1985; 1988) exemplifies the coherence approach with its formal postulates characterizing conservative belief revision.

Modular utility representation for decision-theoretic planning

Specification of objectives constitutes a central issue in knowledge representation for planning. Decision-theoretic approaches require that representations of objectives possess a firm semantics in terms of utility functions, yet provide the flexible compositionality needed for practical preference modeling for planning systems. Modularity, or separability in specification, is the key representational feature enabling this flexibility. In the context of utility specification, modularity corresponds exactly to well-known independence concepts from multiattribute utility theory, and leads directly to approaches for composing separate preference specifications. Ultimately, we seek to use this utility-theoretic account to justify and improve existing mechanisms for specification of preference information, and to develop new representations exhibiting tractable specification and flexible composition of preference criteria.

Semantic parameterization: A process for modeling domain descriptions

Software engineers must systematically account for the broad scope of environmental behavior, including nonfunctional requirements, intended to coordinate the actions of stakeholders and software systems. The Inquiry Cycle Model (ICM) provides engineers with a strategy to acquire and refine these requirements by having domain experts answer six questions: who, what, where, when, how, and why. Goal-based requirements engineering has led to the formalization of requirements to answer the ICM questions about when, how, and why goals are achieved, maintained, or avoided. In this article, we present a systematic process called Semantic Parameterization for expressing natural language domain descriptions of goals as specifications in description logic. The formalization of goals in description logic allows engineers to automate inquiries using who, what, and where questions, completing the formalization of the ICM questions. The contributions of this approach include new theory to conceptually compare and disambiguate goal specifications that enables querying goals and organizing goals into specialization hierarchies. The artifacts in the process include a dictionary that aligns the domain lexicon with unique concepts, distinguishing between synonyms and polysemes, and several natural language patterns that aid engineers in mapping common domain descriptions to formal specifications. Semantic Parameterization has been empirically validated in three case studies on policy and regulatory descriptions that govern information systems in the finance and health-care domains.