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    Game Logic is Strong Enough for Parity Games.Dietmar Berwanger - 2003 - Studia Logica 75 (2):205 - 219.
    We investigate the expressive power of Parikh's Game Logic interpreted in Kripke structures, and show that the syntactical alternation hierarchy of this logic is strict. This is done by encoding the winning condition for parity games of rank n. It follows that Game Logic is not captured by any finite level of the modal -calculus alternation hierarchy. Moreover, we can conclude that model checking for the -calculus is efficiently solvable iff this is possible for Game Logic.
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  2.  33
    Information Tracking in Games on Graphs.Dietmar Berwanger & Łukasz Kaiser - 2010 - Journal of Logic, Language and Information 19 (4):395-412.
    When seeking to coordinate in a game with imperfect information, it is often relevant for a player to know what other players know. Keeping track of the information acquired in a play of infinite duration may, however, lead to infinite hierarchies of higher-order knowledge. We present a construction that makes explicit which higher-order knowledge is relevant in a game and allows us to describe a class of games that admit coordinated winning strategies with finite memory.
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