Journal Article

Intuitionistic propositional logic with Galois connections

Wojciech Dzik, Jouni Järvinen and Michiro Kondo

in Logic Journal of the IGPL

Volume 18, issue 6, pages 837-858
Published in print December 2010 | ISSN: 1367-0751
Published online October 2009 | e-ISSN: 1368-9894 | DOI: https://dx.doi.org/10.1093/jigpal/jzp057
Intuitionistic propositional logic with Galois connections

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In this work, an intuitionistic propositional logic with a Galois connection (IntGC) is introduced. In addition to the intuitionistic logic axioms and inference rule of modus ponens, the logic contains only two rules of inference mimicking the performance of Galois connections. Both Kripke-style and algebraic semantics are presented for IntGC, and IntGC is proved to be complete with respect to both of these semantics. We show that IntGC has the finite model property and is decidable, but Glivenko's Theorem does not hold. Duality between algebraic and Kripke semantics is presented, and a representation theorem for Heyting algebras with Galois connections is proved. In addition, an application to rough L-valued sets is presented.

Keywords: Galois connection; Intuitionistic logic; Algebraic semantics; Kripke-semantics; Representation

Journal Article.  0 words. 

Subjects: Logic

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