Proof Search and Counter-Model Construction for Bi-intuitionistic Propositional Logic with Labelled Sequents

  • Luís Pinto
  • Tarmo Uustalu
Conference paper

DOI: 10.1007/978-3-642-02716-1_22

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5607)
Cite this paper as:
Pinto L., Uustalu T. (2009) Proof Search and Counter-Model Construction for Bi-intuitionistic Propositional Logic with Labelled Sequents. In: Giese M., Waaler A. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2009. Lecture Notes in Computer Science, vol 5607. Springer, Berlin, Heidelberg

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Luís Pinto
    • 1
  • Tarmo Uustalu
    • 2
  1. 1.Centro de MatemáticaUniversidade do MinhoBragaPortugal
  2. 2.Institute of Cybernetics at Tallinn University of TechnologyTallinnEstonia

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