From Axioms to Analytic Rules in Nonclassical Logics

Abstract

We introduce a systematic procedure to transform large classes of (Hilbert) axioms into equivalent inference rules in sequent and hypersequent calculi. This allows for the automated generation of analytic calculi for a wide range of prepositional nonclassical logics including intermediate, fuzzy and substructural logics. Our work encompasses many existing results, allows for the definition of new calculi and contains a uniform semantic proof of cut-elimination for hypersequent calculi.