We provide a theoretical basis for studying termination of (general) logic programs with the Prolog selection rule. To this end we study the class of left terminating programs. These are logic programs that terminate with the Prolog selection rule for all ground goals. We offer a characterization of left terminating positive programs by means of the notion of an acceptable program that provides us with a practical method of proving termination. The method is illustrated by giving a simple proof of termination of the quicksort program for the desired class of goals. Then we extend this approach to the class of general logic programs by modifying the concept of acceptability. We prove that acceptable general programs are left terminating. The converse implication does not hold but we show that under the assumption of nonfloundering from ground goals every left terminating general program is acceptable. Finally, we prove that various ways of defining semantics coincide for acceptable gen...

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 is to demonstrate their utility and simplicity (when they are applicable). We do this by presenting three examples of programs, and a general theorem, all of which are subject to metric methods. One of these is a direct argument that the game program operator T

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this paper appeared as [B]. 1. INTRODUCTION Termination of logic programs is of course of utmost importance. The question whether the top-down evaluation of a goal G terminates with respect to a logic program P is actually underspecified, given the fact that this evaluation may depend on the selection of atoms from goals and on the choice of the program clauses. In this paper termination is considered in the strong sense, i.e. irrespective of the selection of atoms in the goal and of the choice of the program clauses. This is the most demanding notion of termination. Less demanding approaches are: (1) termination for a fixed selection rule and for any choice of program clauses; (2) termination for some selection rule, depending on P, G and annotations on G, and for any choice of program clauses. All approaches can be weakened by requiring termination not for any but only for some

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.

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.

This paper presents an approach for universal left-termination of constraint logic programs, based on approximations. An approximation is basically an algebraic morphism between two constraint structures. By moving from the original domain to natural numbers, we compute inter-argument relations and some control information about a program. By moving from the natural numbers to the booleans, we compute a boolean term called a termination condition such that if the boolean approximation of a goal entails the termination condition, then the Prolog computation tree for that goal is finite.

Current norm-based automatic... In this paper we present a new termination analysis which integrates the various components and produces a set of constraints that, when solvable, identifies successful termination proofs. The proposed method is both efficient and precise. The use of constraint sets enables the propagation of information over all different phases while the need for multiple analyses is considerably reduced.

: We define here a formal notion of finite representation of infinite query answers in logic programs. We apply this notion to Datalog nS (Datalog with n successors): an extension of Datalog capable of representing infinite phenomena like flow of time or plan construction. Predicates in Datalog nS can have arbitrary unary and limited n-ary function symbols in one fixed position. This class of logic programs is known to be decidable. However, least Herbrand models of Datalog nS programs may be infinite and consequently queries may have infinite answers. We present a method to finitely represent infinite least Herbrand models of Datalog nS programs as relational specifications. A relational specification consists of a finite set of facts and a finitely specified congruence relation. A relational specification has the following desirable properties. First, it is explicit in the sense that once it is computed, the original Datalog nS program (and its underlying computational engine) can ...