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Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve in different areas of applications. In this survey of CLP, a primary goal is to give a systematic description of the major trends in terms of common fundamental concepts. The three main parts cover the theory, implementation issues, and programming for applications.

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 reexamine the place and role of stable model semantics in logic programming and contrast it with a least Herbrand model approach to Horn programs. We demonstrate that inherent features of stable model semantics naturally lead to a logic programming system that offers an interesting alternative to more traditional logic programming styles of Horn logic programming, stratified logic programming and logic programming with well-founded semantics. The proposed approach is based on the interpretation of program clauses as constraints. In this setting programs do not describe a single intended model, but a family of stable models. These stable models encode solutions to the constraint satisfaction problem described by the program. Our approach imposes restrictions on the syntax of logic programs. In particular, function symbols are eliminated from the language. We argue that the resulting logic programming system is well-attuned to problems in the class NP, has a well-defined domain of applications, and an emerging methodology of programming. We point out that what makes the whole approach viable is recent progress in implementations of algorithms to compute stable models of propositional logic programs. 1

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We present an abstract framework for default reasoning, which includes Theorist, default logic, logic programming, autoepistemic logic, non-monotonic modal logics, and certain instances of circumscription as special cases. The framework can be understood as a generalisation of Theorist. The generalisation allows any theory formulated in a monotonic logic to be extended by a defeasible set of assumptions. An assumption can be defeated (or "attacked") if its "contrary" can be proved, possibly with the aid of other conflicting assumptions. We show that, given such a framework, the standard semantics of most logics for default reasoning can be understood as sanctioning a set of assumptions, as an extension of a given theory, if and only if the set of assumptions is conflict-free (in the sense that it does not attack itself) and it attacks every assumption not in the set. We propose a more liberal, argumentation-theoretic semantics, based upon the notion of admissible extension in logic pro...

The most general notion of canonical model for a logic program with negation is the one of stable model [9]. In [7] the stable models of a logic program are characterized by the well-supported Herbrand models of the program, and a new fixed point semantics that formalizes the bottom-up truth maintenance procedure of [4] is based on that characterization. Here we focus our attention on the abstract notion of well-supportedness in order to derive sufficient conditions for the existence of stable models. We show that if a logic program \Pi is positive-order-consistent (i.e. there is no infinite decreasing chain w.r.t. the positive dependencies in the atom dependency graph of \Pi) then the Herbrand models of comp(\Pi) coincide with the stable models of \Pi. From this result and the ones of [10] [17] [2] on the consistency of Clark's completion, we obtain sufficient conditions for the existence of stable models for positive-order-consistent programs. Then we show that a negative cycle free ...

Previous researchers have proposed generalizations of Horn clause logic to support negation and non-determinism as two seperate extensions. In this paper, we show that the stable model semantics for logic programs provides a unified basis for the treatment of both concepts. First, we introduce the concepts of partial models, stable modds, strongly founded models and deterministic models and other interesting classes of partial models and study their relationships. We show that the maximal deterministic model of a program is a subset of the intersection of all its stable models and that the well-founded model of a program is a subset of its maximal deterministic model. Then, we show that the use of stable models subsumes the use of the non-deterministic choice construct in LDL and provides an alternative definition of the semantics of this construct. Finally, we provide a constructive definition for stable models with the introduction of a procedure, called backtracking fixpoint, that noneteterminisfically constructs a total stable model, if such a model exists.

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