A Cut-Free Simple Sequent Calculus for Modal Logic S5

Francesca Poggiolesi (1)

1 IHPST - Institut d'Histoire et de Philosophie des Sciences et des Techniques

In this paper, we present a simple sequent calculus for the modal propositional logic S5. We prove that this sequent calculus is theoremwise equivalent to the Hilbert-style system S5, that it is contraction-free and cut-free, and finally that it is decidable. All results are proved in a purely syntactic way.

Mots clés: modal logic; mathematics

Domaines: Histoire, Philosophie et Sociologie des sciences

Francesca Poggiolesi. A Cut-Free Simple Sequent Calculus for Modal Logic S5. The review of symbolic logic, 2008, 1 (1), pp.3-15. ⟨halshs-00775809⟩