Computing finite models by reduction to function-free clause logic

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Computing finite models by reduction to function-free clause logic (2007)

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by Peter Baumgartner , Alexander Fuchs , Hans De Nivelle , Cesare Tinelli

Venue:	Journal of Applied Logic
Citations:	32 - 9 self

BibTeX

@ARTICLE{Baumgartner07computingfinite,
    author = {Peter Baumgartner and Alexander Fuchs and Hans De Nivelle and Cesare Tinelli},
    title = {Computing finite models by reduction to function-free clause logic},
    journal = {Journal of Applied Logic},
    year = {2007},
    volume = {2007}
}

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Abstract

Recent years have seen considerable interest in procedures for computing finite models of first-order logic specifications. One of the major paradigms, MACE-style model building, is based on reducing model search to a sequence of propositional satisfiability problems and applying (efficient) SAT solvers to them. A problem with this method is that it does not scale well because the propositional formulas to be considered may become very large. We propose instead to reduce model search to a sequence of satisfiability problems consisting of function-free first-order clause sets, and to apply (efficient) theorem provers capable of deciding such problems. The main appeal of this method is that first-order clause sets grow more slowly than their propositional counterparts, thus allowing for more space efficient reasoning. In this paper we describe our proposed reduction in detail and discuss how it is integrated into the Darwin prover, our implementation of the Model Evolution calculus. The results are general, however, as our approach can be used in principle with any system that decides the satisfiability of function-free first-order clause sets. To demonstrate its practical feasibility, we tested our approach on all satisfiable problems from the TPTP library. Our methods can solve a significant subset of these problems, which overlaps but is not included in the subset of problems solvable by state-of-the-art finite model builders such as Paradox and Mace4.

Keyphrases

finite model function-free clause logic model search function-free first-order clause set space efficient state-of-the-art finite model builder first-order logic specification considerable interest satisfiable problem propositional formula significant subset major paradigm main appeal sat solver propositional satisfiability problem tptp library model evolution calculus first-order clause set satisfiability problem recent year darwin prover mace-style model building theorem provers propositional counterpart practical feasibility

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