Article

Theorem proving modulo based on Boolean equational procedures

Authors:

José MeseguerAuthors Info & Claims

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

Pages 337 - 351

Published: 07 April 2008 Publication History

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.

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Cited By

Gutiérrez RMeseguer JRocha C(2012)Order-Sorted equality enrichments modulo axiomsProceedings of the 9th international conference on Rewriting Logic and Its Applications10.1007/978-3-642-34005-5_9(162-181)Online publication date: 24-Mar-2012
https://dl.acm.org/doi/10.1007/978-3-642-34005-5_9

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Theorem proving modulo based on Boolean equational procedures

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cover image Guide Proceedings

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

April 2008

397 pages

ISBN:354078912X

Editors:
Rudolf Berghammer
Christian-Albrechts-Universität zu Kiel, Institut für Informatik, Kiel, Germany
,
Bernhard Möller
Universität Augsburg, Institut für Informatik, Augsburg, Germany
,
Georg Struth
University of Sheffield, Department of Computer Science, Sheffield, UK

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CrossSoft
HSH Nordbank AG
ARIVA.DE AG

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 07 April 2008

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Cited By

Gutiérrez RMeseguer JRocha C(2012)Order-Sorted equality enrichments modulo axiomsProceedings of the 9th international conference on Rewriting Logic and Its Applications10.1007/978-3-642-34005-5_9(162-181)Online publication date: 24-Mar-2012
https://dl.acm.org/doi/10.1007/978-3-642-34005-5_9

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