Abduction in Logic Programming started in the late 80s, early 90s, in an attempt to extend logic programming into a framework suitable for a variety of problems in Artificial Intelligence and other areas of Computer Science. This paper aims to chart out the main developments of the field over the last ten years and to take a critical view of these developments from several perspectives: logical, epistemological, computational and suitability to application. The paper attempts to expose some of the challenges and prospects for the further development of the field.

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.

The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules in a declarative manner, and a defeasible argumentation inference mechanism for warranting the entailed conclusions. In DeLP an argumentation formalism will be used for deciding between contradictory goals. Queries will be supported by arguments that could be defeated by other arguments. A query q will succeed when there is an argument A for q that is warranted, i. e. the argument A that supports q is found undefeated by a warrant procedure that implements a dialectical analysis. The defeasible argumentation basis of DeLP allows to build applications that deal with incomplete and contradictory information in dynamic domains. Thus, the resulting approach is suitable for representing agent’s knowledge and for providing an argumentation based reasoning mechanism to agents.

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...

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

Logic programs with positive occurrences of negation as failure have recently been introduced as a subset of the logic of minimal belief and negation as failure (MBNF). A unique feature of such programs, which other traditional logic programs lack, is that the minimality of answer sets does not hold. We reveal in this paper that this property is important for applying logic programming to represent abduction and inclusive disjunctions. With its rich expressiveness, however, the computational complexity of such extended programs is shown to remain in the same complexity class as normal disjunctive programs. Through the elimination of negation as failure from programs, computation of such extended programs is realized using bottom-up model generation techniques. A simple translation of programs into autoepistemic logic is also presented. 1 Introduction Most of semantics of logic programs proposed so far satisfy the principle of minimality in some sense. For example, the least model sema...

Abduction-- from observations and a theory, find using hypotheses an explanation for the observations -- gained increasing interest during the last years. This form of reasoning has wide applicability in different areas of computer science; in particular, it has been recognized as an important principle of common-sense reasoning. In this paper, we define a general abduction model for logic programming, where the inference operator (i.e., the semantics to be applied on programs), can be specified by the user. Advanced forms of logic programming have been proposed as valuable tools for knowledge representation and reasoning. We show that logic programming semantics can be more meaningful for abductive reasoning than classical inference by providing examples from the area of knowledge representation and reasoning. The main part of the paper is devoted to an extensive study of the computational complexity of the principal problems in abductive reasoning, which are: Given an inst...

Abstract not found

The focus of this paper is nonmonotonic reasoning as it relates to logic programming. I discuss the pre-history of nonmonotonic reasoning starting from approximately 1958. I then review the research that has been accomplished in the areas of circumscription, default theory, modal theories and logic programming. The overview includes the major results developed including complexity results that are known about the various theories. I then provide a summary which includes an assessment of the field and what must be done to further research in nonmonotonic reasoning and logic programming. 1 Introduction Classical logic has played a major role in computer science. It has been an important tool both for the development of architecture and of software. Logicians have contended that reasoning, as performed by humans, is also amenable to analysis using classical logic. However, workers in the field of artificial 1 This paper is an updated version of an invited Banquet Address, First Interna...