Cut-elimination and proof-search for bi-intuitionistic logic using nested sequents

Linda Postniece

Computer Science Laboratory
Australian National University

Thursday, 2 October 2008, 14:00
Cybernetica Bldg (Akadeemia tee 21), room B101

Slides from the talk [pdf]

Abstract: Bi-intuitionistic logic is the extension of intuitionistic logic with exclusion, a connective dual to implication. Bi-intuitionistic logic was introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her subsequent "cut-free" sequent calculus has recently been shown by Uustalu to fail cut-elimination. We propose a new sequent calculus for bi-intuitionistic logic which sits somewhere between display calculi and traditional sequent calculi by using nested sequents. Our calculus enjoys a simple (purely syntactic) cut-elimination proof as do display calculi. But it has an easily derivable variant calculus which is amenable to automated proof search as are (some) traditional sequent calculi. As far as we know, our new calculus is the first sequent calculus for bi-intuitionistic logic which uses no semantic additions like labels, which has a purely syntactic cut-elimination proof, and which can be used naturally for backwards proof-search. (Joint work with Rajeev Goré and Alwen Tiu.)

Tarmo Uustalu
Last update 2.10.2008