Representing and Reasoning about Game Strategies

TL;DR

This paper introduces a formal language for representing and reasoning about game strategies, extending existing frameworks with temporal and preference modalities, and demonstrates its application through formal semantics and automated reasoning methods.

Contribution

It develops a novel logical language for game strategies that integrates temporal reasoning and preferences, with formal semantics and implementation examples.

Findings

Language supports reasoning about game strategies

Formal semantics aligns with state-transition models

Implementation via Situation Calculus and Answer Set Programming

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.