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.

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.

SLD resolution with negation as finite failure (SLDNF) reflects the procedural interpretation of predicate calculus as a programming language and forms the computational basis for Prolog systems. Despite its advantages for stack-based memory management, SLDNF is often not appropriate for query evaluation for three reasons: a) it may not terminate due to infinite positive recursion; b) it may not terminate due to infinite recursion through negation; c) it may repeatedly evaluate the same literal in a rule body, leading to unacceptable performance. We address three problems fir a goal-oriented query evaluation of general logic programs by presenting tabled evaluation with delaying (SLG resolution).

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.

1 Introduction The perfect model semantics [ABW88, VG89b, Prz88a, Prz89b] provides an attractive alternative to the traditionally used semantics of logic programs based on Clark's completion of the program [Cla78, Llo84, Fit85, Kun87]. Perfect models are minimal models of the program, which can be equivalently described as iterated least fixed points of natural operators [ABW88, VG89b], as iterated least models of the program [ABW88, VG89b] or as preferred models with respect to a natural priority relation [Prz88a, Prz89b]. As a result, the perfect model semantics is not only very intuitive, but it also has been proven equivalent to suitable forms of all four major formalizations of non-monotonic reasoning in AI (see [Prz88b]) and is used in existing database [Zan88] and truth maintenance systems. Additionally, the perfect model semantics eliminates some serious drawbacks of Clark's semantics [Prz89b] and admits a natural sound and complete procedural mechanism, called SLSresolution [...

Almost all constraint logic programming systems include negation, yet nowhere has a sound operational model for negation in CLP been discussed. The SLDNF approach of only allowing ground negative subgoals to execute is very restrictive in constraint logic programming where most variables appearing in a derivation never become ground. By describing a scheme for constructive negation in constraint logic programming we give a sound and complete operational model for negation in these languages. Constructive negation was first formulated for logic programming in the Herbrand Universe and involves introducing disequality constraints. Constraint logic programming thus provides a much more natural framework for describing constructive negation. In this paper we describe a framework for constructive negation for constraint logic programming over arbitrary structures which is sound and complete with respect to the three-valued consequences of the completion of a program. Through this descriptio...

The paper is a general overview of an approach to the semantics of logic programs whose aim is finding notions of models which really capture the operational semantics, and are therefore useful for defining program equivalences and for semantics-based program analysis. The approach leads to the introduction of extended interpretations which are more expressive than Herbrand interpretations. The semantics in terms of extended interpretations can be obtained as a result of both an operational (top-down) and a fixpoint (bottom-up) construction. It can also be characterized from the model-theoretic viewpoint, by defining a set of extended models which contains standard Herbrand models. We discuss the original construction modeling computed answer substitutions, its compositional version and various semantics modeling more concrete observables. We then show how the approach can be applied to several extensions of positive logic programs. We finally consider some applications, mainly in the area of semantics-based program transformation and analysis.

Abstract not found

One of the most important and difficult problems in logic programming is the problem of finding a suitable declarative or intended semantics for logic programs. The importance of this problem stems from the declarative character of logic programming, whereas its difficulty can be largely attributed to the non-monotonic character of the negation operator used in logic programs. The problem can therefore be viewed as the problem of finding a suitable formalization of the type of non-monotonic reasoning used in logic programming. In this paper we introduce a semantics of logic programs based on the class PERF(P) of all, not necessarily Herbrand, perfect models of a program P and we show that the proposed semantics is not only natural but it also combines many of the desirable features of previous approaches, at the same time eliminating some of their drawbacks. For a positive program P, the class PERF(P) of perfect models coincides with the class MIN(P) of all minimal models of P. The per...

We introduce global SLS-resolution, a procedural semantics for well-founded negation as defined by Van Gelder, Ross and Schlipf. Global SLS-resolution extends Przymusinski 's SLS-resolution, and may be applied to all programs, whether locally stratified or not. 1 Global SLS-resolution is defined in terms of global trees, a new data structure representing the dependence of goals on derived negative subgoals. We prove that global SLS-resolution is sound with respect to the well-founded semantics, and complete for non-floundering queries. While not effective in general, global SLS-resolution is effective for classes of "acyclic" programs, and can be augmented with a memoing device to be effective for all function-free programs. This research was supported by the National Science Foundation under grant IRI-87-22886, by a grant from IBM Corporation, and by the United States Air Force Office of Scientific Research under contract AFOSR-88-0266. A preliminary version of this paper was presen...