Michael Gelfond

Classical negation in logic programs and disjunctive databases

An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic programs by including classical negation, in addition to negation-as-failure. The semantics of such extended programs is based on the method of stable models. The concept of a disjunctive database can be extended in a similar way. We show that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available. Computationally, classical negation can be eliminated from extended programs by a simple preprocessor. Extended programs are identical to a special case of default theories in the sense of Reiter.

Representing action and change by logic programs

Abstract We represent properties of actions in a logic programming language that uses both classical negation and negation as failure. The method is applicable to temporal projection problems with incomplete information, as well as to reasoning about the past. It is proved to be sound relative to a semantics of action based on states and transition functions.

Logic programming and knowledge representation

Abstract In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider extensions of the language of definite logic programs by classical (strong) negation, disjunction, and some modal operators and show how each of the added features extends the representational power of the language. We also discuss extensions of logic programming allowing abductive reasoning, meta-reasoning and reasoning in open domains. We investigate the methodology of using these languages for representing various forms of nonmonotonic reasoning and for describing knowledge in specific domains. We also address recent work on properties of programs needed for successful applications of this methodology such as consistency, categoricity and complexity.

An A-Prolog Decision Support System for the Space Shuttle

The goal of this paper is to test if a programming methodology based on the declarative language A-Prolog and the systems for computing answer sets of such programs, can be successfully applied to the development of medium size knowledge-intensive applications. We report on a successful design and development of such a system controlling some of the functions of the Space Shuttle.

Logic programming and knowledge representation—The A-Prolog perspective

Abstract In this paper we give a short introduction to logic programming approach to knowledge representation and reasoning. The intention is to help the reader to develop a ‘feel’ for the fields history and some of its recent developments. The discussion is mainly limited to logic programs under the answer set semantics. For understanding of approaches to logic programming built on well-founded semantics, general theories of argumentation, abductive reasoning, etc., the reader is referred to other publications.

On the relationship between circumscription and negation as failure

Abstract The aim of this paper is to investigate two powerful methods of handling negative information in logic-based knowledge representation systems: the logical minimization in the form of circumscription and the negation as failure rule, formalized by various closures (or completions) of original theories. We suggest a new, more powerful form of the negation as failure rule and describe an important class of theories for which this form of negation as failure is equivalent to particular forms of circumscription. These results establish a close relationship between the two important formalizations of nonmonotonic reasoning and provide a syntactic characterization of the corresponding circumscriptive theories. This allows us to apply existing methods of deduction using various negation as failure rules to answering queries in a broad class of circumscriptive theories.

Reasoning agents in dynamic domains

The paper discusses an architecture for intelligent agents based on the use of A-Prolog- a language of logic programs under the answer set semantics. A-Prolog is used to represent the agents reasoning tasks. We outline how these tasks can be reduced to answering questions about properties of simple logic programs and demonstrate the methodology of constructing these programs.

Probabilistic Reasoning With Answer Sets

We give a logic programming based account of probability and describe a declarative language P-log capable of reasoning which combines both logical and probabilistic arguments. Several non-trivial examples illustrate the use of P-log for knowledge representation.

Probabilistic reasoning with answer sets

This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give several non-trivial examples and illustrate the use of P-log for knowledge representation and updating of knowledge. We argue that our approach to updates is more appealing than existing approaches. We give sufficiency conditions for the coherency of P-log programs and show that Bayes nets can be easily mapped to coherent P-log programs.

Representing actions: Laws, observations and hypotheses

Abstract We propose a modificationL 1 of the action description languageA. The languageL 1 allows representation of hypothetical situations and hypothetical occurrence of actions (as inA) as well as representation of actual occurrences of actions and observations of the truth values of fluents in actual situations. The corresponding entailment relation formalizes various types of common-sense reasoning about actions and their effects not modeled by previous approaches. As an application of L1 we also present an architecture for intelligent agents capable of observing, planning and acting in a changing environment based on the entailment relation of L1 and use logic programming approximation of this entailment to implement a planning module for this architecture. We prove the soundness of our implementation and give a sufficient condition for its completeness.