Augmenting ATL with strategy contexts

We study the extension of the alternating-time temporal logic (ATL) with strategy contexts: contrary to the original semantics, in this semantics the strategy quantifiers do not reset the previously selected strategies. We show that our extension ATLsc is very expressive, but that its decision problems are quite hard: model checking is k -EXPTIME-complete when the formula has k nested strategy quantifiers; satisfiability is undecidable, but we prove that it is decidable when restricting to turn-based games. Our algorithms are obtained through a very convenient translation to QCTL (the computation-tree logic CTL extended with atomic quantification), which we show also applies to Strategy Logic, as well as when strategy quantification ranges over memoryless strategies.