CS Theory Seminars


Relating sequent calculi for bi-intuitionistic propositional logic

Tarmo Uustalu

Institute of Cybernetics

Thursday, 9 September 2010, 14:00
Cybernetica Bldg (Akadeemia tee 21), room B 101

Abstract

Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic.

In this paper, we compare three sequent calculi for bi-intuitionistic propositional logic: (1) a basic standard-style sequent calculus that restricts the premises of implication-right and exclusion-left inferences to be single-conclusion resp. single-assumption and is incomplete without the cut rule, (2) the calculus with nested sequents by Goré et al., where a complete class of cuts is encapsulated into special „unnest“ rules and (3) a cut-free labelled sequent calculus derived from the Kripke semantics of the logic. We show that these calculi can be translated into each other and discuss the ineliminable cuts of the standard-style sequent calculus.

(Joint work with Luís Pinto.)

Viimati muutnud: 2010/09/09 11:59