Kripke Completeness of Infinitary Predicate Multimodal Logics

Abstract

Kripke completeness of some infinitary predicate modal logics is presented. More precisely, we prove that if a normal modal logic L above K is D-persistent and universal, the infinitary and predicate extension of L with ⋀Fω1 and BF i⋀Kripke complete, where BFω1 and BF denote the formulas i∈ω pi ⊃ i∈ω pi and ∀x ϕ ⊃ ∀xϕ, respectively. The results include the completeness of extensions of standard modal logics such as K, and its extensions by the schemata T, B, 4, 5, D, and their combinations. The proof is obtained by extending the correspondence between the representation of modal algebras and the completeness of propositional modal logic to infinite. © 1999 by the University of Notre Dame. All rights reserved.