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A Rule-Based Framework for Building Superposition-Based Decision Procedures

Elena Tushkanova 1, 2 Alain Giorgetti 2, 1 Christophe Ringeissen 2 Olga Kouchnarenko 2, 1
2 CASSIS - Combination of approaches to the security of infinite states systems
FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174), Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
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.
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Submitted on : Wednesday, November 7, 2012 - 5:18:50 PM
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Elena Tushkanova, Alain Giorgetti, Christophe Ringeissen, Olga Kouchnarenko. A Rule-Based Framework for Building Superposition-Based Decision Procedures. WRLA 2012 - 9th International Workshop on Rewriting Logic and Its Applications, Mar 2012, Tallinn, Estonia. pp.221-239, ⟨10.1007/978-3-642-34005-5_12⟩. ⟨hal-00749576⟩



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