Syntax

We assume the syntax of classical propositional logic as used in the chapters above. Additional we have the following two rules: If ${\displaystyle A}$ is a formula

${\displaystyle {\begin{matrix}&&\diamond A{\mbox{ and}}\\&&\square A\end{matrix}}}$

are formulae.

The symbols ${\displaystyle \diamond }$ and ${\displaystyle \Box }$ stand traditionally for possibility and necessity; in the context of temporal logic they stand for always and eventually, so that ${\displaystyle \diamond A}$ stands for ${\displaystyle A}$ is eventually true and ${\displaystyle \Box A}$ for ${\displaystyle A}$ is always true.