Contraction-free calculi for modal logics S5 and KD45

Abstract

It is known that termination and backtracking are among the most important problems in constructing derivations in non-classical logics. In this paper contractionfree and backtracking-free sequent calculi for modal logics S5 and KD45 are presented and founded. These are index-style sequent calculi with some specific indexed axioms. The main new ideas in considered calculi are to use metavariables (along with natural numbers) as elements of indexes and to numerate by different natural number all the positive occurrences of modality 2.

Keywords

• modal logic
• sequent calculus
• termination
• backtracking
• contraction-free