A tableau calculus for propositional intuitionistic logic with a refined treatment of nested implications

Abstract

Since 1993, when Hudelmaier developed an O-space decision procedure for propositional Intuitionistic Logic, a lot of work has been done to improve the efficiency of the related proof-search algorithms. In this paper a tableau calculus using the signs T, F and F c with a new set of rules to treat signed formulas of the kind T → C) is provided. The main feature of the calculus is the reduction of both the non-determinism in proof-search and the width of proofs with respect to Hudelmaier's one. These improvements have a significant influence on the performances of the implementation.

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References found in this work

Modal Logic.Alexander Chagrov - 1997 - Oxford, England: Oxford University Press.
Investigations Into Logical Deduction.Gerhard Gentzen - 1964 - American Philosophical Quarterly 1 (4):288 - 306.
Investigations Into Logical Deduction.Gerhard Gentzen, M. E. Szabo & Paul Bernays - 1970 - Journal of Symbolic Logic 35 (1):144-145.
Contraction-Free Sequent Calculi for Intuitionistic Logic.Roy Dyckhoff - 1992 - Journal of Symbolic Logic 57 (3):795-807.

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