Kripke semantics is a type of interpretation for several non-classical logics. Most notably, modal logic.
A kripke frame is an ordered pair where:
- is a set of points or worlds that represent possible worlds.
- is a relation that relates worlds to other worlds.
One could create a directed graph out of a kripke frame, where is used as the set of nodes and is used as the vertices.
A kripke frame is an ordered pair (G,R,v), where:
- is a kripke frame.
- is a mapping , where is the language of the formal system and is a set of truth values. Alternatively, it is a relation on the set of worlds and the language of the formal system..
Let , then is used to denote . When it is clear what the kripke model is, one sometimes uses .
Some authors use instead of . The resulting notation is