The purpose of this paper is to study the fundamental mechanism humans use in argumentation and its role in different major approaches to commonsense reasoning in AI and logic programming. We present three novel results: We develop a theory for argumentation in which the acceptability of arguments is precisely defined. We show that logic programming and nonmonotonic reasoning in AI are different forms of argumentation. We show that argumentation can be viewed as a special form of logic programming with negation as failure. This result introduces a general method for generating metainterpreters for argumentation systems. 1.

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.

Abstract. In this paper we explore the thesis that the role of argumentation in practical reasoning in general and legal reasoning in particular is to justify the use of defeasible rules to derive a conclusion in preference to the use of other defeasible rules to derive a conflicting conclusion. The defeasibility of rules is expressed by means of non-provability claims as additional conditions of the rules. We outline an abstract approach to defeasible reasoning and argumentation which includes many existing formalisms, including default logic, extended logic programming, non-monotonic modal logic and auto-epistemic logic, as special cases. We show, in particular, that the “admissibility ” semantics for all these formalisms has a natural argumentationtheoretic interpretation and proof procedure, which seem to correspond well with informal argumentation. In the admissibility semantics there is only one way for one argument to attack another, namely by undermining one of its non-provability claims. In this paper, we show how other kinds of attack between arguments, specifically how rebuttal and priority attacks, can be reduced to the undermining of non-provability claims. 1.

The well-founded semantics and the stable model semantics capture intuitions of the skeptical and credulous semantics in nonmonotonic reasoning, respectively. They represent the two dominant proposals for the declarative semantics of deductive databases and logic programs. However, neither semantics seems to be suitable for all applications. We have developed an efficient implementation of goal-oriented effective query evaluation under the well-founded semantics. It produces a residual program for subgoals that are relevant to a query, which contains facts for true instances and clauses with body literals for undefined instances. This paper presents a simple method of stable model computation that can be applied to the residual program of a query to derive answers with respect to stable models. The method incorporates both forward and backward chaining to propagate the assumed truth values of ground atoms, and derives multiple stable models through backtracking. Users are ab...

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...

this paper, we generalize the program transformation techniques of [17] for non-abductive programs to deal with abductive frameworks. We introduce a new translation from an abductive logic program into a positive disjunctive program, and show that the belief models of an abductive program can be characterized by the fixpoint closure of the transformed disjunctive program. In the transformation, both negative hypotheses through negation as failure and positive hypotheses from the abducibles are dealt with uniformly. This fixpoint characterization is further extended to a fixpoint semantics for abductive extended disjunctive programs, i.e., abductive programs that permit classical negation as well as disjunctions. For a procedural aspect of our fixpoint semantics, we also show that a model generation procedure for positive disjunctive programs can be used as a sound and complete procedure for computing belief models for function-free and range-restricted programs.

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...

Stable models have been first introduced in the domain of total interpretations (T- stable models), where the existence of multiple T-stable models for the same program provides a powerful mechanism to express non-determinism. Stable models have been later extended to the domain of partial interpretations (P-stable models). In this paper, we show that the presence of multiple P-stable models need not be a direct manifestation of non-determinism, for it can be instead an expression of assorted degrees of undefinedness. To separate the two factors, non-determinism and undefinedness, this paper introduces the notion of deterministic stable models and strictly non-deterministic ones. Deterministic stable models form an interesting family, having a lattice structure where the well-founded model serves as the bottom; the top of the lattice, the maximum deterministic stable model, resolves differences between any two P-stable models in the family. On the other hand, every two models in a fam...

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