transition formula

A transition formula’s free variables range over $V\cup V^{\prime }$ (as opposed to a state formula).

It denotes a set of transitions $(s,s^{\prime })$, with $(s,s^{\prime })\models \phi$ iff $\sigma \models \phi$ where $\sigma (v)=s(v)$ for v in V and $\sigma (v)=s^{\prime }(v)$ for v in V’