Proof Search and Counter-Model Construction for Bi-intuitionistic Propositional Logic with Labelled Sequents
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BibTeX
@MISC{Pinto_proofsearch,
author = {Luís Pinto and Tarmo Uustalu},
title = {Proof Search and Counter-Model Construction for Bi-intuitionistic Propositional Logic with Labelled Sequents},
year = {}
}
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Abstract
Abstract. Bi-intuitionistic logic is a conservative extension of intuitionistic logic with a connective dual to implication, called exclusion. We present a sound and complete cut-free labelled sequent calculus for bi-intuitionistic propositional logic, BiInt, following S. Negri’s general method for devising sequent calculi for normal modal logics. Although it arises as a natural formalization of the Kripke semantics, it is does not directly support proof search. To describe a proof search procedure, we develop a more algorithmic version that also allows for counter-model extraction from a failed proof attempt. 1
