Local Intuitionistic Modal Logics and Their Calculi
Philippe Balbiani, Han Gao, Çiğdem Gencer, Nicola Olivetti · Lecture notes in computer science · 2024
Abstract We investigate intuitionistic modal logics with locally interpreted $$\square $$ □ and $$\lozenge $$ ◊ . The basic logic LIK is stronger than constructive modal logic WK and incomparable with intuitionistic modal logic IK. We propose an axiomatization of LIK and some of its extensions. Additionally, we present bi-nested calculi for LIK and these extensions, providing both a decision procedure and a procedure of finite countermodel extraction.