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Representing and Building Models for Decidable Subclasses of Equational Clausal Logic

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Abstract

We develop new techniques for the automated construction of models for subclasses of equational clausal logic. The models are represented by some specific class of rewrite rules. We show that the evaluation of arbitrary first-order formulae in these interpretations is a decidable problem. As an example of an application, we consider the class \({\mathcal{OCC}1\mathcal{N}}\) , a decidable subclass of first-order clausal logic without equality. In the equational case, \({\mathcal{OCC}1\mathcal{N}}\) is undecidable, but it is known to be decidable if all the equational literals are ground. We extend this result to a class of clause sets possibly containing nonground equational literals. The algorithms for extracting models from positively disconnected saturated sets proposed by Fermüller and Leitsch are extended in order to handle the full ordering restrictions of the resolution/paramodulation calculus.

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  1. Centre National de la Recherche Scientifique, Laboratoire Leibniz, IMAG, 46 Avenue Felix Viallet, 38031, Grenoble cedex, France

    N. Peltier

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Peltier, N. Representing and Building Models for Decidable Subclasses of Equational Clausal Logic. J Autom Reasoning 33, 133–170 (2004). https://doi.org/10.1007/s10817-004-5555-7

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