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.

This paper presents a formal semantic basis for the termination analysis of logic programs. The semantics exhibits the termination properties of a logic program through its binary unfoldings --- a possibly infinite set of binary clauses. Termination of a program P and goal G is determined by the absence of an infinite chain in the binary unfoldings of P starting with G. The result is of practical use as basing termination analysis on a formal semantics facilitates both the design and implementation of analyzers. A simple Prolog interpreter for binary unfoldings coupled with an abstract domain based on symbolic norm constraints is proposed as an implementation vehicle. We illustrate its application using two recently proposed abstract domains. Both techniques are implemented using a standard CLP(R) library. The combination of an interpreter for binary unfoldings and a constraint solver simplifies the design of the analyzer and improves its efficiency significantly. 1 Introduction This ...

This paper describes a system implemented in SICStus Prolog for automatically checking left termination of logic programs. Given a program and query, the system answers either that the query terminates or that there may be non-termination. The system can use any norm of a wide family of norms. It can handle automatically most of the examples found in the literature on termination of logic programs, and about half of the programs in the benchmarks of [5]. The algorithm employed by the system consists of three main parts: instantiation analysis (i.e., rigidity analysis), constraint inference, and construction of the query-mapping pairs associated with the program and query. Each of these parts generalizes earlier work related to termination analysis. 1 Introduction Termination analysis of logic programs has been the focus of intensive research in recent years. Systems for automatic termination analysis are proposed, for example, in [15, 20, 22]. Methodologies and techniques for proving ...

We provide a uniform and simplified presentation of the methods of Bezem [Bez93] (first published as [Bez89]) and of Apt and Pedreschi [AP93] (first published as [AP90]) for proving termination of logic and Prolog programs. Then we show how these methods can be refined so that they can be used in a modular way.

We introduce topologies on spaces of interpretations which extend and generalise the query and positive query topologies of Batarekh and Subrahmanian. We study continuity in these topologies of the immediate consequence map associated with any normal logic program and provide necessary and sufficient conditions for continuity to hold. We relate these ideas to (i) computational power of programs; (ii) canonical programs; (iii) the declarative semantics of definite programs; (iv) Maher's down continuous programs; (v) the decency thesis of Jaffar, Lassez and Maher, and (vi) compactness of sets of fixed points and models. 1 Introduction The classical approach to the study of fixed point semantics of definite logic programs P utilises two main facts: (1) The set I J L of all interpretations of the underlying language L based on a given preinterpretation J forms a complete lattice under the partial order of set inclusion. (2) The immediate consequence map T P defined on I J L is latti...

One facet of the question of integration of Logic and Connectionist Systems, and how these can complement each other, concerns the points of contact, in terms of semantics, between neural networks and logic programs. In this paper, we show that certain semantic operators for propositional logic programs can be computed by feedforward connectionist networks, and that the same semantic operators for first-order normal logic programs can be approximated by feedforward connectionist networks. Turning the networks into recurrent ones allows one also to approximate the models associated with the semantic operators. Our methods depend on a wellknown theorem of Funahashi, and necessitate the study of when Funahasi's theorem can be applied, and also the study of what means of approximation are appropriate and significant.

work in the ESPRIT project DiSCiPl. The project aims at devising advanced tools for debugging of constraint logic programs. Acentral problem in program development is obtaining a program which satis es the user's expectations. When considering a given program, a natural question is then whether or not it

Since the late eighties, much progress has been made in the theory of termination analysis for logic programs. However, from a practical point of view, the significance of much of the work on termination is hard to judge, since experimental evaluations rarely get published. Here we describe and evaluate a termination analyzer for Mercury, a strongly typed and moded logicfunctional programming language. Mercury's high degree of referential transparency and the guaranteed availability of reliable mode information simplify the termination analysis of Mercury compared with that of other logic programming languages. We describe our termination analyzer, which uses a variant of a method developed by Plumer. It deals with full Mercury, including modules, declarative input/output, the foreign language interface, and higher-order features. In spite of these obstacles, it produces high-quality termination information, comparable to the results recently obtained by Lindenstrauss and Sagiv. Most i...

this paper, we present a transformational approach for proving termination of logic programs by reducing the termination problem of logic programs to that of term rewriting systems. The termination problem of term rewriting systems has been well studied and many useful techniques and tools have been developed for proving termination of term rewriting systems. The prime motivation of our approach is to facilitate the use of this vast source of termination techniques and tools in proving termination of logic programs.

. We consider how mode (such as input and output) and termination properties of typed higher-order constraint logic programming languages may be declared and checked effectively. The systems that we present have been validated through an implementation and numerous case studies. 1 Introduction Just like other paradigms logic programming benefits tremendously from types. Perhaps most importantly, types allow the early detection of errors when a program is checked against a type specification. With some notable exceptions most type systems proposed for logic programming languages to date (see [18]) are concerned with the declarative semantics of programs, for example, in terms of many-sorted, order-sorted, or higher-order logic. Operational properties of logic programs which are vital for their correctness can thus neither be expressed nor checked and errors will remain undetected. In this paper we consider how the declaration and checking of mode (such as input and output) and termina...