The method of valuations in modal logic

In this paper we present a decision method for Kripke’s modal calculus K, obtained from a new 0–1 valuation semantics for this calculus which, by means of a weakening of the truth conditions concerning the modal operation of necessity, dispense with central notions of Kripkean semantics, such as the notion of an accessibility relation between worlds and of a plurality of worlds in the same model. The valuation semantics can be easily extended to many other calculi containing K, such as T, S4, etc. It can also be adapted to weaker modal calculi as well as to deontic and temporal logics. (More about this kind of semantics can be found, for example, in [1] and in [2].)