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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-modelconstruction and syntactic cut-elimination. Linear nested sequents thus providethe minimal amount of nesting necessary to provide an adequate proof-theory formodal logics containing converse. As a bonus, this yields a cut-free calculusfor symmetric modal logic KB.

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