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On computability by logic programs

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Abstract

The problem of computational completeness of Horn clause logic programs is revisited. The standard results on representability of all computable predicates by Horn clause logic programs are not related to the real universe on which logic programs operate. SLD-resolution, which is the main mechanism to execute logic programs, may give answer substitutions with variables. As the main result we prove that computability by Horn clause logic programs is equivalent to standard computability over the Herbrand universe with variables. The semantics we use isS-semantics introduced by Falaschi et al. [3]. As an application of the main result we prove the existence of a metainterpreter for a sublanguage of real Prolog, written in the language of Horn clauses with the S-semantics. We also show that the traditional semantics of Prolog do not reflect its computational behavior from the viewpoint of recursion theory.

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Authors and Affiliations

  1. Computer Science Department, Uppsala University, S-75105, Uppsala, Sweden

    Andrei Voronkov

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  1. Andrei Voronkov
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Additional information

This article is a revised version of [13]. The work was essentially done during author's visit to ECRC.

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Voronkov, A. On computability by logic programs. Ann Math Artif Intell 15, 437–456 (1995). https://doi.org/10.1007/BF01536404

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