Intuitionistic propositional logic with Galois connections

W. Dzik, J. Jarvinen, M. Kondo
2009 Logic Journal of the IGPL  
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
more » ... o'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.
doi:10.1093/jigpal/jzp057 fatcat:gm5gcpwp6famnliqg7isktvuvi