Generic Modal Cut Elimination Applied to Conditional Logics

Abstract

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