It was later adapted to other non-classical logics, most importantly intuitionistic logic.

A Kripke frame or modal frame is a pair , where W is a non-empty set, and R is a binary relation on W.

Jaakko Hintikka gave a semantics in his papers introducing epistemic logic that is a simple variation of Kripke's semantics, equivalent to the characterisation of valuations by means of maximal consistent sets.

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