Game-Theoretic Semantics for Alternating-Time Temporal Logic

TL;DR

This paper develops game-theoretic semantics for ATL, allowing truth to be characterized by winning strategies in evaluation games, and introduces variants with resource limitations that are equivalent to standard semantics.

Contribution

It unifies object-level and meta-level game semantics for ATL and introduces resource-bounded variants that are proven equivalent to classical semantics.

Findings

Unifies ATL semantics with game-theoretic evaluation games.

Proves equivalence of unbounded and ordinal-bounded GTS to standard semantics.

Introduces a finitely bounded semantics with natural logical and game-theoretic interpretation.

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 is 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 falsifier in the semantic evaluation game. We introduce and analyse an unbounded and (ordinal) bounded GTS and prove these to be equivalent to the standard (Tarski-style) compositional semantics. We show that in these both versions of GTS, truth of ATL formulae can always be determined in finite time, i.e., without constructing infinite paths. We also introduce a non-equivalent finitely bounded semantics and argue that it is natural from both logical and game-theoretic perspectives.