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On the declarative and procedural semantics of logic programs

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Abstract

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 perfect model semantics is shown to be equivalent to the semantics of McCarthy's circumscription and is also equivalent to the remaining three major formalizations of non-monotonic reasoning in artificial intelligence-Reiter's closed world assumption, Moore's autoepistemic logic and Reiter's default theorythus establishing a closer link between the areas of logic programming and non-monotonic reasoning.

We also define a generalization of SLD-resolution, called SLS-resolution and we prove that SLS-resolution is sound and complete with respect to the perfect model semantics.

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  1. Department of Mathematics, University of Texas at El Paso, 79968, El Paso, TX, USA

    Teodor C. Przymusinski

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Przymusinski, T.C. On the declarative and procedural semantics of logic programs. J Autom Reasoning 5, 167–205 (1989). https://doi.org/10.1007/BF00243002

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  • DOI: https://doi.org/10.1007/BF00243002

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