Sequent calculi and decidability for intuitionistic hybrid logic

Abstract

In this paper we study the proof theory of the first constructive version of hybrid logic called Intuitionistic Hybrid Logic ( IHL) in order to prove its decidability. In this perspective we propose a sequent-style natural deduction system and then the first sequent calculus for this logic. We prove its main properties like soundness, completeness and also the cut-elimination property. Finally we provide, from our calculus, the first decision procedure for IHL and then prove its decidability.