We consider two sequent calculi for tense logic in which the syntactic judgements are nested sequents, i.e., a tree of traditional onesided sequents built from multisets of formula...
We consider an extension of bi-intuitionistic logic with the traditional modalities , , and from tense logic Kt. Proof theoretically, this extension is obtained simply by extendin...
Bi-intuitionistic logic is the extension of intuitionistic logic with exclusion, a connective dual to implication. Cut-elimination in biintuitionistic logic is complicated due to t...
We see a systematic set of cut-free axiomatisations for all the basic normal modal logics formed by some combination the axioms d, t, b, 4, 5. They employ a form of deep inference ...