Implication and deduction in some intuitionistic modal logics (1)

Abstract

We sttidy the deductive properties of the System IM4 of intuitionistic modal logic, paying special attention to the implicative ones. This System is the intuítionistic counterpart of Lewis' S4 and its models are the topological pseudo-Boolean algebras. Its abstract deductive strueture is analogous to that of pseudo-Boolean algebras but here w.ith respect to new implicative operations. These satisfy the Deduction Theorem and allow us to find implicative characterizations of several types of deductive Systems (such as irreducible, maximal, prime) and some related conoepts from universal algebra (simplicity, semisimplicity, radical)...