Game-Theoretic Semantics for Alternating-Time Temporal Logic

We introduce several versions of game-theoretic semantics (GTS) for Alternating-Time Temporal Logic (ATL). In GTS, truth is defined in terms of existence of a winning strategy in a semantic evaluation game, and thus the game-theoretic perspective appears in the framework of ATL on two semantic levels: on the object level, in the standard semantics of the strategic operators, and on the meta-level, where game-theoretic logical semantics can be applied to ATL. We unify these two perspectives into semantic evaluation games specially designed for ATL. The game-theoretic perspective enables us to identify new variants of the semantics of ATL, based on limiting the time resources available to the verifier and falsier in the semantic evaluation game. We introduce and analyse unbounded and bounded GTS and prove these to be equivalent to the standard (Tarski style) compositional semantics. We also introduce a non-equivalent finitely bounded semantics and argue that it is natural from both logical and game-theoretic perspectives.

Authors

• Valentin Goranko

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