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

Abstract

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 15445The contribution was presented at :http://www.pricai.org/ Abstract. This paper presents a logical framework that extends the Game Description Language with coalition operators from Alternatingtime Temporal Logic and prioritised strategy connectives. Our semantics is built upon the standard state transition model. The new framework allows us to formalise van Benthem's game-oriented principles in multiplayer games, and formally derive Weak Determinacy and Zermelo's Theorem for two-player games. We demonstrate with a real-world game how to use our language to specify a game and design a strategy, and how to use our framework to verify a winning/no-losing strategy. Finally, we show that the model-checking problem of our logic is in 2EXPTIME with respect to the size of game structure and the length of formula, which is no worse than the model-checking problem in ATL ⋆ .

Synthesizing human-friendly optimal strategies in board games

“…Representing strategies by FFTs in a logical form is similar to work by Jiang et al [16] and Silva et al [17]. Here s |= φ means that φ is true in s using standard semantics for propositional logic.…”

Game Description Logic with Integers: A GDL Numerical Extension

“…GDL with Imperfect Information and Introspection (GDL-III) is an extension of GDL-II to include epistemic games, which are characterized by rules that depend on the knowledge of players [14,15]. In order to model how agents can cooperate to achieve a desirable goal, Jiang et al (2014) present a framework to combine GDL with the coalition operators from Alternating-time Temporal Logic and prioritized strategy connectives [5].…”