Logic for Computer Scientists/Modal Logic/Syntax

Syntax
We assume the syntax of classical propositional logic as used in the chapters above. Additional we have the following two rules: If $$A$$ is a formula $$\begin{matrix} & & \diamond A \mbox{ and} \\

& & \square  A \end{matrix}$$ are formulae.

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