ABSTRACT
A wff α of modal logic is valid (with respect to a class ^o f frames) iff, for every (W,R) G #, and every model (W,R.V) based on (W,R), V(α,w) = 1 for every w G W. In this chapter we shall show how to test wff for validity in K, D, T, S4 and S5, when the relevant classes of frames are the following: For K, & is the class of all frames without restriction. For D, ^ i s the class of all serial frames; for T, all reflexive frames; for S4, all reflexive and transitive frames and finally for S5, all equivalence frames, i.e. all frames which are reflexive, transitive and symmetrical. So let S be one of these systems, and let & be the appropriate class of frames. In what follows, by an S-model we shall mean a model based on a frame in the class of frames appropriate for S.
