Model checking of strategic ability under imperfect information is known to be hard. In this paper, we propose translations of ATLir formulae that provide lower and upper bounds for their truth values, and are cheaper to verify than the original specifications. Most interestingly, the lower approximation is provided by a fixpoint expression that uses a nonstandard variant of the next-step ability operator. We show the correctness of the translations, establish their computational complexity, and validate the approach by experiments with a scalable scenario of Bridge play.
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