Valuation Semantics for S4

Abstract

This expository paper presents an application, to the modal logic S4, of the valuation semantics technique proposed by Loparić for the basic normal modal logic K. In previous works we presented a valuation semantics for the minimal temporal logic Kt and several other systems modal and temporal logic. How to deal with S4, however, was left as an open problem—although we arrived at a working definition of \(A_1,\ldots ,A_n\)-valuations, we were not able to prove an important lemma for correctness. In this paper we solve this, presenting valuations for S4.