Representing and Reasoning about Game Strategies

Abstract

Abstract. As a contribution to the challenge of building game-playing AI systems, we develop and analyse a formal language for representing and reasoning about strategies. Our logical language builds on the existing general Game Description Language (GDL) and extends it by a standard modality for linear time along with two dual connectives to express preferences when combining strategies. The semantics of the language is provided by a standard state-transition model. As such, problems that require reasoning about games can be solved by the standard methods for reasoning about actions and change. We also endow the language with a specific semantics by which strategy formulas are understood as move recommendations for a player. To illustrate how our formalism supports automated reasoning about strategies, we demonstrate two example methods of implementation: first, we formalise the semantic interpretation of our language in conjunction with game rules and strategy rules in the Situation Calculus; second, we show how the reasoning problem can be solved with Answer Set Programming.

GDL Meets ATL: A Logic for Game Description and Strategic Reasoning

“…The prioritised disjunctive connective ▽ is borrowed from [12]. The formula ϕ 1 ▽ϕ 2 has to be read as "achieve ϕ 1 first; if it is impossible, achieve ϕ 2 ''.…”

“…The formula ϕ 1 ▽ϕ 2 has to be read as "achieve ϕ 1 first; if it is impossible, achieve ϕ 2 ''. Different from [12], we define the prioritised conjunction △ by the prioritised disjunction:…”

“…To address the second problem, a number of approaches have been proposed for representing game strategies [2,7,[10][11][12]. The simplest way to represent a game strategy is to express a strategy as an action so that simple strategies can be combined into more complicated strategies using PDL connectives [7,11].…”

“…The simplest way to represent a game strategy is to express a strategy as an action so that simple strategies can be combined into more complicated strategies using PDL connectives [7,11]. Zhang and Thielscher recently introduced another approach to represent game strategies [12]. With their framework, a strategy is represented as a logical formula in GDL.…”

“…We need a comprehensive logical language and associated inference mechanism to define, compare and reason about strategies. In this paper, we propose a logical language by extending GDL with coalition operators and prioritised connectives [1,9,12]. Inherited from GDL, the proposed logical language can describe any finite perfect information game.…”