Situation Calculus Game Structures and GDL

Giuseppe De Giacomo, Yves Lespérance, Adrian R. Pearce

Abstract: We present a situation calculus-based account of multi-players synchronous games in the style of general game playing. Such games can be represented as action theories of a special form, situation calculus synchronous game structures (SCSGSs), in which we have a single action tick whose effects depend on the combination of moves selected by the players. Then one can express properties of the game, e.g., winning conditions, playability, weak and strong winnability, etc. in a first-order alternating-time μ-calculus. We discuss verification in this framework considering computational effectiveness. We also show that SCSGSs can be considered as a first-order variant of the Game Description Language (GDL) that supports infinite domains and possibly non-terminating games. We do so by giving a translation of GDL specifications into SCSGSs and showing its correctness. Finally, we show how a player's possible moves can be specified in a Golog-like programming language.