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Non-Horn clause logic programming without contrapositives

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Abstract

We present an extension of Prolog-style Horn clause logic programming to full first order logic. This extension has some advantages over other such extensions that have been proposed. We compare this method with the model elimination strategy which Stickel has recently implemented very efficiently, and with Loveland's extension of Prolog to near-Horn clauses. This new method is based on the author's “simplified problem reduction format” but permits a better control of the splitting rule than does the simplified problem reduction format. In contrast to model elimination, this new method does not require the use of contrapositives of clauses, permitting a better control of the search. This method has been implemented in C Prolog and has turned out to be a respectable and surprisingly compact first-order theorem prover. This implementation uses depth-first iterative deepening and caching of answers to avoid repeated solution of the same subgoal. We show that the time and space used by this method are polynomial functions of certain natural parameters of the search space, unlike other known methods. We discuss the relation of these upper bounds to Savitch's theorem relating nondeterministic time to deterministic space.

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Authors and Affiliations

  1. Department of Computer Science, University of North Carolina at Chapel Hill, 27514, Chapel Hill, North Carolina, USA

    David A. Plaisted

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  1. David A. Plaisted
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Additional information

This research was supported in part by the National Science Foundation under grant DCR-8516243.

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Plaisted, D.A. Non-Horn clause logic programming without contrapositives. J Autom Reasoning 4, 287–325 (1988). https://doi.org/10.1007/BF00244944

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  • DOI: https://doi.org/10.1007/BF00244944

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