First-Order Logic with Counting for General Game Playing

Abstract

General Game Players (GGPs) are programs which can play an arbitrary game given only its rules and the Game Description Language (GDL) is a variant of Datalog used in GGP competitions to specify the rules. GDL inherits from Datalog the use of Horn clauses as rules and recursion, but it too requires stratification and does not allow to use quantifiers. We present an alternative formalism for game description which is based on first-order logic (FO). States of the game are represented by relational structures, legal moves by structure rewriting rules guarded by FO formulas, and the goals of the players by formulas which extend FO with counting. The advantage of our formalism comes from more explicit state representationcand from the use of quantifiers in formulas. We show how to exploit existential quantification in players' goals to generate heuristics for evaluating positions in the game. The derived heuristics are good enough for a basic alpha-beta agent to win against state of the art GGP.