A rule-based framework for building superposition-based decision procedures

Authors:
Elena Tushkanova;Alain Giorgetti;Christophe Ringeissen;Olga Kouchnarenko
Affiliations:
Inria, Villers-les-Nancy, France,CNRS FEMTO-ST and University of Franche-Comté, Besançon, France;Inria, Villers-les-Nancy, France,CNRS FEMTO-ST and University of Franche-Comté, Besançon, France;Inria, Villers-les-Nancy, France;Inria, Villers-les-Nancy, France,CNRS FEMTO-ST and University of Franche-Comté, Besançon, France
Venue:
WRLA'12 Proceedings of the 9th international conference on Rewriting Logic and Its Applications
Year:
2012

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Abstract

This paper deals with decision procedures specified as inference systems. Among them we focus on superposition-based decision procedures. The superposition calculus is a refutation-complete inference system at the core of all equational theorem provers. In general this calculus provides a semi-decision procedure that halts on unsatisfiable inputs but may diverge on satisfiable ones. Fortunately, it may also terminate for some theories of interest in verification, and thus it becomes a decision procedure. To reason on the superposition calculus, a schematic superposition calculus has been studied, for instance to automatically prove termination. This paper presents an implementation in Maude of these two inference systems. Thanks to this implementation we automatically derive termination of superposition for a couple of theories of interest in verification.