Alternating-time temporal logic

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In computer science, alternating-time temporal logic, or ATL, is a branching-time temporal logic that extends computation tree logic (CTL) to multiple players.^[1] ATL naturally describes computations of multi-agent systems and concurrent games.^[2] Quantification in ATL is over program-paths that are possible outcomes of games.^[3] ATL uses alternating-time formulas to construct model-checkers in order to address problems such as receptiveness, realizability, and controllability.

One can write logical formulas in ATL such as ${\displaystyle \langle \langle \{a,b\}\rangle \rangle Fp}$ that expresses the fact that agents a and b have a strategy to ensure that the property p holds in the future, whatever the other agents of the system are performing.

ATL* is the extension of ATL, as CTL* extends CTL. ATL* allows to write more complex temporal objectives, for instance ${\displaystyle \langle \langle \{a,b\}\rangle \rangle (Fp\land Gq)}$. Belardinelli et al. proposes a variant of ATL on finite traces.^[4] ATL has been extended with context, in order to store the current strategies played by the agents. ATL* is extended by strategy logic.

ATL has been generalized to include epistemic features. In 2003, van der Hoek and Woodridge proposed ATEL: the logic ATL augmented with an epistemic operator from epistemic logic.^[5] In 2004, Pierre-Yves Schobbens proposed variants of ATL with imperfect recall.^[6]

One cannot express properties about individual objectives in ATL. That is why, in 2010, Chatterjee, Henzinger and Piterman introduced strategy logic, a first-order logic in which strategies are first-order citizens.^[7] Strategy logic subsumes both ATL and ATL*.

• Linear temporal logic