Synchronous Games in the Situation Calculus

We develop a situation calculus-based account of multi-player synchronous games. These are represented as action theories called situation calculus synchronous game structures (SCSGSs) that involve a single action tick whose effects depend on the combination of moves chosen by the players. Properties of games, e.g., winning conditions, playability, weak and strong winnability, etc. can be expressed in a first-order variant of alternating-time mu-calculus. Computationally effective verification can be performed. SCSGSs can be viewed as a variant of the Game Description Language (GDL) where states are represented by first-order theories.