Sequent Calculi for some subintuitionistic Logics

Abstract

This Paper investigate sequent calculi for certain weak subintuitionistic logics. We establish that weakening and contraction are height-preserving admissible for each of these calculi, and we provide a syntactic proof for the admissibility of the cut rule for most of these sequent calculi. We also demonstrate the equivalence of these calculi to their corresponding axiomatic systems, thereby confirming their soundness and completeness with respect to neighbourhood semantics.