Authors: Dirk Pattinson ; Lutz Schröder

We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies also to a wide variety of logics outside the realm of normal modal logic. We give extensive example instantiations of our framework to various conditional logics. For these, we obtain fully internalised calculi which are substantially simpler than those known in the literature, along with leaner proofs of cut elimination and complexity. In one case, conditional logic with modus ponens and conditional excluded middle, cut elimination and complexity were explicitly stated as open in the literature.

• 03B45 - Modal logic (including the logic of norms)
• 03B47 - Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
• 03F05 - Cut-elimination and normal-form theorems
• 03F52 - Proof-theoretic aspects of linear logic and other substructural logics

• 1 zbMATH Open