Sequent Calculi for some subintuitionistic Logics

TL;DR

This paper develops sequent calculi for weak subintuitionistic logics, proving key admissibility properties and establishing their soundness and completeness via syntactic and semantic methods.

Contribution

It introduces new sequent calculi for subintuitionistic logics and proves their admissibility and equivalence to axiomatic systems.

Findings

Weakening and contraction are height-preserving admissible

Cut rule is admissible in most calculi

Calculi are sound and complete with respect to neighbourhood semantics

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.