Glivenko Type Theorems for Intuitionistic Modal Logics
Author: Bezhanishvili, G.
Source: Studia Logica, Volume 67, Number 1, February 2001 , pp. 89-109(21)
Abstract:In this article we deal with Glivenko type theorems for intuitionistic modal logics over Prior's MIPC. We examine the problems which appear in proving Glivenko type theorems when passing from the intuitionistic propositional logic Intto MIPC. As a result we obtain two different versions of Glivenko's theorem for logics over MIPC. Since MIPCcan be thought of as a one-variable fragment of the intuitionistic predicate logic Q-Int, one of the versions of Glivenko's theorem for logics over MIPCis closely related to that for intermediate predicate logics obtained by Umezawa  and Gabbay . Another one is rather surprising.
Keywords: Heyting algebras; completely modalized formulas; dense elements; essentially negative formulas; essentially negative strongly modalized formulas; intuitionistic modal logics; monadic Heyting algebras; regular elements; strongly modalized formulas; super-dense elements
Document Type: Regular Paper
Affiliations: Department of Mathematical Sciences New Mexico State University Las Cruces, NM 88003-0001, USA email@example.com
Publication date: February 1, 2001