Generic Modal Cut Elimination Applied to Conditional Logics

Details Generic Modal Cut Elimination Applied to Conditional Logics Generic Modal Cut Elimination Applied to Conditional Logics

2010-11-15

arxiv.org/abs/1011.3479v2

LMCS 7 (1:4) 2011

Computer Science

Logic in Computer Science

Scientific paper

10.2168/LMCS-7(1:4)2011

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.

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