We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the proof-theoretic and model-theoretic issues and the relationships between them.

In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten- sions of the language of definite logic programs by classical (strong) negation, disjunc- tion, and some modal operators and show how each of the added features extends the representational power of the language.

this paper we show, however, that stationary expansions can be equivalently defined in terms of classical, 2-valued logic. As a byproduct, we obtain a simpler and more natural description of stationary expansions.

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 field's 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 build on well-founded semantics, general theories of argumentation, abductive reasoning, etc., the reader is referred to other publications.

. At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire and Nicolas in Toulouse, France, which culminated in a workshop held in Toulouse, France in 1977. It is appropriate, then to provide an assessment as to what has been achieved in the twenty years since the field started as a distinct discipline. In this retrospective I shall review developments that have taken place in the field, assess the contributions that have been made, consider the status of implementations of deductive databases and discuss the future of work in this area. 1 Introduction As described in [234], the use of logic and deduction in databases started in the late 1960s. Prominent among the developments was the work by Levien and Maron [202, 203, 199, 200, 201] and Kuhns [1...

Recently several authors have stressed and showed the importance of having a second kind of negation in logic programs for use in deductive databases, knowledge representation, and nonmonotonic reasoning [6, 7, 8, 9, 13, 14, 15, 24]. Different semantics for logic programs extended with :-negation (extended logic programs) have appeared [1, 4, 6, 9, 11, 12, 17, 19, 24] but, contrary to what happens with semantics for normal logic programs, there is no general comparison among them, specially in what concerns the use and meaning of the newly introduced :-negation. The goal of this paper is to contrast a variety of these semantics in what concerns their use and meaning of :-negation, and its relation to classical negation and to the default negation of normal programs, here denoted by not : To this purpose we define a parametrizeable schema to encompass and characterize a diversity of proposed semantics for extended logic programs, where the parameters are two: one the axioms AX: defin...

The purpose of this paper is to investigate the methodology of reasoning with prioritized defaults in the language of logic programs under the answer set semantics. We present a domain independent system of axioms, written as an extended logic program, which defines reasoning with prioritized defaults. These axioms are used in conjunction with a description of a particular domain encoded in a simple language allowing representation of defaults and their priorities. Such domain descriptions are of course domain dependent and should be specified by the users. We give sufficient conditions for consistency of domain descriptions and illustrate the use of our system by formalizing various examples from the literature. Unlike many other approaches to formalizing reasoning with priorities ours does not require development of the new semantics of the language. Instead, the meaning of statements in the domain description is given by the system of (domain independent) axioms. We believe that in ...

Our purpose is to exhibit a modular systematic method of representing non-- monotonic reasoning problems with the Well Founded Semantics WFS of extended logic programs augmented with eXplicit negation (WFSX), augmented by its Contradiction Removal Semantics (CRSX) when needed. We apply this semantics, and its contradiction removal semantics counterpart, to represent non-monotonic reasoning problems. We show how to cast in the language of logic programs extended with explicit negation such forms of non-monotonic reasoning as defeasible reasoning, abductive reasoning and hypothetical reasoning and apply them to such different domains of knowledge representation as hierarchies and reasoning about actions. We then abstract a modular systematic method of representing non-monotonic problems in a logic programming semantics comprising two forms of negation avoiding some drawbacks of other proposals, with which we relate our work.

this paper we extend the language A and its translation to allow reasoning about the effects of concurrent actions. The logic programming formalization of situation calculus with concurrent actions presented in the paper is of independent interest and may serve as a test bed for the investigation of various transformations and logic programming inference mechanisms. ! 1. INTRODUCTION

Our aim in this article is to supplement the set of strong properties introduced in the preceding article ([Dix94]) with a set of weak principles in order to characterize semantics of logic programs. In [Dix94] we introduced our point of view: we observed that all semantics induce in a natural way a sceptical non-monotonic entailment relation SEM scept . We ask for the properties of these sceptical relations and use them to describe all possible semantics. We collect in this paper serious shortcomings of some semantics proposed recently. Their strange behaviour led us to formulate in a natural way certain principles to avoid these problems. We argue that any well-behaved semantics should satisfy these principles. The main results state that our list of weak principles is complete in the following sense: any well-behaved-semantics is an extension of the well-founded semantics WFS and coincides for stratified programs with Apt, Blair, and Walker's supported model M supp P . We also...