In logic, the term temporal logic is used to describe any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time. It is sometimes also used to refer to tense logic, a particular modal logic-based system of temporal logic introduced by Arthur Prior in the 1960s.

Temporal logic was first studied in depth by Aristotle, and his writings are filled with a crude form of first order temporal modal binary logic. Any logic which uses the existential quantifier or the universal quantifier, is said to be a first order logic. Any logic which views time as a sequence of states, is a temporal logic, and any logic which uses only two truth values, is a binary logic.

Consider the statement, "I am hungry." Though its meaning is constant in time, the truth value of the statement can vary in time. Sometimes the statement is true, and sometimes the statement is false, but the statement is never true and false simultaneously. In a temporal logic, statements can have a truth value which can vary in time. Contrast this with an atemporal logic, which can only handle statements whose truth value is constant in time. The three basic temporal operators are: Always, sometimes, and never.

Computational tree logic (CTL) and Linear temporal logic (LTL) are two examples of temporal logics.

See also

• Anthony Galton, "Temporal Logic" http://plato.stanford.edu/entries/logic-temporal/ in the Stanford Encyclopedia of Philosophy http://plato.stanford.edu/ .
• Temporal logic in finite-state verification
• Hybrid logic
• Temporal Logic of Actions (TLA)
• Important publications in formal verification (including the use of temporal logic in formal verification)