**Kripke semantics** is a type of interpretation for several non-classical logics. Most notably, modal logic.

## Kripke FrameEdit

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.

## Kripke modelEdit

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..

### NotationsEdit

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