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Temporal logic is a branch of symbolic logic which is concerned with problems on propositions that have truth values dependent on time. Temporal logic is considered a variant of modal logic, which is a branch of logic dealing with propositions that can be expressed as a set of possible worlds. Temporal logic is used to touch all approaches to reasoning and representation based on time.
Applications of temporal logic include use in reasoning in philosophical issues based on time, as a language in artificial language for encoding temporal knowledge, and as tool for formal analysis, specification and verification of hardware and software requirements of computer applications and systems.
One of the salient features of temporal propositions is that it mostly has either implicit or explicit references to time conditions. This is in contrast to classical logic, which focuses on timeless propositions. Temporal logic is one of the best and most appropriate means for reasoning with time-related propositions, thanks to the temporal quantifiers. Although classical logic can deal with temporal properties, the formulas often tend to be complicated as points of time need to be represented.
The concept of temporal logic was first introduced by Arthur Prior in 1960 under "tense logic" which was further broadened by other computer scientists and logicians. Temporal logic is not focused on the truth or falsity of formulas, rather is focused on the formulas which remain true through the flow of time, even if valuation is altered.
Temporal logic has two types of operators: modal operators and logical operators. Model operators are largely used in computation tree logic and linear temporal logic, whereas logical operators are mostly truth-functional operators. Signal temporal logic, interval temporal logic, metric interval temporal logic, linear temporal logic, computational tree logic and others form parts of temporal logic.