## FANDOM

174 Pages

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 $(G,R)$ where:

• $G$ is a set of points or worlds that represent possible worlds.
• $R$ is a relation that relates worlds to other worlds.

One could create a directed graph out of a kripke frame, where $G$ is used as the set of nodes and $R$ is used as the vertices.

## Kripke modelEdit

A kripke frame is an ordered pair (G,R,v), where:

• $(G,R)$ is a kripke frame.
• $v$ is a mapping $v:G \times \mathcal{L} \to \{t,f\}$, where $\mathcal{L}$ is the language of the formal system and $\{t,f\}$ is a set of truth values. Alternatively, it is a relation $v \subseteq G \times \mathcal{L}$ on the set of worlds and the language of the formal system..

### NotationsEdit

Let $\mathcal{M}=(G,R,v)$, then $\mathcal{M}, w \models \phi$ is used to denote $v(w,\phi)=t$. When it is clear what the kripke model is, one sometimes uses $w \models \phi$.

Some authors use $\Vdash$ instead of $v$. The resulting notation is $w \Vdash \phi$