tidslogiske

Tidslogiske, or temporal logic in English, is a formal framework for reasoning about time. It extends standard propositional or first-order logic with operators that refer to moments in time, such as what is true now, what will always be true in the future, or what eventually becomes true. This allows precise statements about how truth values of propositions unfold over time.

There are two main traditions in temporal logic. Linear-time temporal logic (LTL) describes a single sequence of events, using operators such as X (next), G (always in the future), F (eventually), and U (until). Branching-time temporal logic (CTL and related formalisms) reasons about multiple possible futures at once and uses path quantifiers like A (for all paths) and E (there exists a path) in combination with temporal operators. Variants such as CTL* combine elements of both approaches.

Historically, temporal logic emerged in the mid-20th century with foundational ideas from Arthur Prior. It was formalized and popularized in computer science during the 1970s and 1980s, notably by Amir Pnueli, who applied temporal logic to the verification of programs, and by Clarke and Emerson, who helped develop model checking for finite-state systems. Since then, temporal logic has become a core tool in formal verification, hardware and software design, and the study of reactive systems. It also finds applications in linguistics for the semantics of tense and aspect and in AI planning for reasoning about sequences of actions.

See also temporal logic, modal logic, and model checking.