Sequent Calculi for Global Modal Consequence Relations

Abstract

The global consequence relation of a normal modal logic $$\Lambda $$ is formulated as a global sequent calculus which extends the local sequent theory of $$\Lambda $$ with global sequent rules. All global sequent calculi of normal modal logics admits global cut elimination. This property is utilized to show that decidability is preserved from the local to global sequent theories of any normal modal logic over $$\mathsf {K4}$$ . The preservation of Craig interpolation property from local to global sequent theories of any normal modal logic is shown by proof-theoretic method.