Temporal logic of actions

Temporal logic of actions (TLA) is a logic developed by Leslie Lamport, which combines temporal logic with a logic of actions.
It is used to describe behaviours of concurrent systems.
Details.
Statements in temporal logic are of the form formula_1, where "A" is an action and "t" contains a subset of the variables appearing in "A". An action is an expression containing primed and non-primed variables, such as formula_2. The meaning of the non-primed variables is "the variable's value in this state". The meaning of primed variables is "the variable's value in the next state".
The above expression means the value of "x" "today", plus the value of "x" "tomorrow" times the value of y "today", equals the value of "y" "tomorrow".
The meaning of formula_1 is that either A is valid now, or the variables appearing in t do not change. This allows for stuttering steps, in which none of the program variables change their values.