Theorem proving modulo based on Boolean equational procedures

Authors:
Camilo Rocha;José Meseguer
Affiliations:
Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL;Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL
Venue:
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
Year:
2008

Citing 14
Cited 1

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Abstract

Deduction with inference rules modulo computation rules plays an important role in automated deduction as an effective method for scaling up. We present four equational theories that are isomorphic to the traditional Boolean theory and show that each of them gives rise to a Boolean decision procedure based on a canonical rewrite system modulo associativity and commutativity. Then, we present two modular extensions of our decision procedure for Dijkstra-Scholten propositional logic to the Sequent Calculus for First Order Logic and to the Syllogistic Logic with Complements of L. Moss. These extensions take the form of rewrite theories that are sound and complete for performing deduction modulo their equational parts and exhibit good mechanization properties. We illustrate the practical usefulness of this approach by a direct implementation of one of these theories in Maude rewriting logic language, and automatically proving a challenge benchmark in theorem proving.