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Simplification Rules for Intuitionistic Propositional Tableaux

Simplification Rules for Intuitionistic Propositional Tableaux Simpli cation Rules for Intuitionistic Propositional Tableaux ` MAURO FERRARI, Universita degli Studi dell ™Insubria ` CAMILLO FIORENTINI, Universita degli Studi di Milano ` GUIDO FIORINO, Universita degli Studi di Milano-Bicocca The implementation of a logic requires, besides the de nition of a calculus and a decision procedure, the development of techniques to reduce the search space. In this article we introduce some simpli cation rules for Intuitionistic propositional logic that try to replace a formula with an equi-satis able œsimpler  one with the aim to reduce the search space. Our results are proved via semantical techniques based on Kripke models. We also provide an empirical evaluation of their impact on implementations. Categories and Subject Descriptors: F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic ”Proof theory; Mechanical theorem proving General Terms: Theory Additional Key Words and Phrases: Decision procedures, intuitionistic logic, simpli cation rules, tableau calculi ACM Reference Format: Ferrari, M., Fiorentini, C., and Fiorino, G. 2012. Simpli cation rules for intuitionistic propositional tableaux. ACM Trans. Comput. Logic 13, 2, Article 14 (April 2012), 23 pages. DOI = 10.1145/2159531.2159536 http://doi.acm.org/10.1145/2159531.2159536 1. INTRODUCTION It is well known that the effective implementation of a logic requires, besides the de http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Simplification Rules for Intuitionistic Propositional Tableaux

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References (20)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2012 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/2159531.2159536
Publisher site
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Abstract

Simpli cation Rules for Intuitionistic Propositional Tableaux ` MAURO FERRARI, Universita degli Studi dell ™Insubria ` CAMILLO FIORENTINI, Universita degli Studi di Milano ` GUIDO FIORINO, Universita degli Studi di Milano-Bicocca The implementation of a logic requires, besides the de nition of a calculus and a decision procedure, the development of techniques to reduce the search space. In this article we introduce some simpli cation rules for Intuitionistic propositional logic that try to replace a formula with an equi-satis able œsimpler  one with the aim to reduce the search space. Our results are proved via semantical techniques based on Kripke models. We also provide an empirical evaluation of their impact on implementations. Categories and Subject Descriptors: F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic ”Proof theory; Mechanical theorem proving General Terms: Theory Additional Key Words and Phrases: Decision procedures, intuitionistic logic, simpli cation rules, tableau calculi ACM Reference Format: Ferrari, M., Fiorentini, C., and Fiorino, G. 2012. Simpli cation rules for intuitionistic propositional tableaux. ACM Trans. Comput. Logic 13, 2, Article 14 (April 2012), 23 pages. DOI = 10.1145/2159531.2159536 http://doi.acm.org/10.1145/2159531.2159536 1. INTRODUCTION It is well known that the effective implementation of a logic requires, besides the de

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ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery

Published: Apr 1, 2012

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