Cut-Elimination and Proof Search for Bi-Intuitionistic Tense Logic

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 extending an existing sequent calculus for bi-intuitionistic logic with typical inference rules for the modalities used in display logics. As it turns out, the resulting calculus, LBiKt, seems to be more basic than most intuitionistic tense or modal logics considered in the literature, in particular, those studied by Ewald and Simpson, as it does not assume any a priori relationship between the modal operators and . We recover Ewald's intuitionistic tense logic and Simpson's intuitionistic modal logic by modularly extending LBiKt with additional structural rules. The calculus LBiKt is formulated in a variant of display calculus, using a form of sequents called nested sequents. Cut elimination is proved for LBiKt, using a technique similar to that used in display calculi. As in display calculi, the inferenc...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Rajeev Goré, Linda Postniece, Alwen Tiu
• Keywords: Calculus, CORR 2010, Education, Inference Rules, Logic