Proof Search and Counter-Model Construction for Bi-intuitionistic Propositional Logic with Labelled Sequents
- 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
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.
Unable to display preview. Download preview PDF.