Syntactic cut-elimination and backward proof-search for tense logic via linear nested sequents (Extended version)

07/02/2019

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by   Rajeev Goré, et al.

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We give a linear nested sequent calculus for the basic normal tense logic Kt. We show that the calculus enables backwards proof-search, counter-model construction and syntactic cut-elimination. Linear nested sequents thus provide the minimal amount of nesting necessary to provide an adequate proof-theory for modal logics containing converse. As a bonus, this yields a cut-free calculus for symmetric modal logic KB.