Definition
Tense logic is the logic of time — the formal study of reasoning with it was the case that and it will be the case that. Ordinary logic treats statements as simply true or false. But 'it is raining' can be true now and false an hour from now. Tense logic adds operators that handle this shift in truth value across time.
Pioneered by Arthur Prior, tense logic reuses the machinery of modal logic. Where modal logic quantifies over possible worlds, tense logic quantifies over moments of time, treating past and future as directions in which to look.
Why it matters
How it works
Tense logic introduces operators usually written P (it was the case that) and F (it will be the case that), with their universal partners — it always was, it always will be. Truth is evaluated at a time, and a tensed claim is true at a time when the underlying claim holds at some appropriate earlier or later time.
This works because moments of time can be ordered just as possible worlds can be related by accessibility. The interesting choices concern the structure of that ordering. Is time a single line, with one fixed future? Or does it branch toward the future, leaving genuine alternatives open? Tense logic does not settle that question, but it makes the alternatives precise — which is exactly what leads to the theory of branching time.