We propose a non-standard semantics for Alternating-time Temporal Logic with incomplete information, for which no commonly accepted semantics has been proposed yet. In our semantics, formulae are interpreted over sets of states rather than single states. We also propose a new epistemic operator for practicalʺ or constructiveʺ knowledge, and we show that the new language is strictly more expressive than existing solutions, while it retains the same model checking complexity. Finally, we study properties of constructive knowledge and other operators in a non-standard semantics like this. Keywords: Alternating-time Temporal Logic, strategic ability, incomplete information, epistemic logic.
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