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Strategy representation and reasoning has been one of the most active research areas in AI and multi-agent systems. Representative strategic logics are ATL and the more expressive Strategy Logic SL which reasons about strategies explicitly. In this paper, by a simple extension of the situation calculus with a strategy sort, we develop a general framework for strategy representation and reasoning for complete information games. This framework can be used to compactly represent both concurrent and turn-based possibly infinite game structures, specify the internal structure of strategies, reason about strategies explicitly, and reason about strategic abilities of coalitions under commitments to strategy specifications. We show that our framework is strictly more expressive than SL, and inspired by the work of De Giacomo et al. on bounded action theories, give a decidable fragment of our framework.
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