A modal analog for Glivenko’s theorem and its applications

Abstract

This paper gives a modal analog for Glivenko’s Theorem. It is proved that (◊A → ◊B) ϵ K4 iff (◊A → ◊B) ϵ S5. Some applicationsof this analog are obtained. A formula f is called an NP-formula if f is built up on its own subformulas of the form ◊B. It is shown that if f is an NP- formula then the logic ∧ + ϕ is decidable or has the finite model property if ∧ ⊇ K4 and A has this property. © University of Notre Dame. All rights reserved.