Game-Theoretic Semantics for Alternating-Time Temporal Logic

Abstract

We introduce 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 novel 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 falsifier in the semantic evaluation game; we introduce and analyse an 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.

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Cite this paper

@inproceedings{Goranko2016GameTheoreticSF, title={Game-Theoretic Semantics for Alternating-Time Temporal Logic}, author={Valentin Goranko and Antti Kuusisto and Raine R{\"{o}nnholm}, booktitle={AAMAS}, year={2016} }