This paper proposes a logical framework for representing and reasoning about imperfect information games. We first extend Game Description Language (GDL) with the standard epistemic operators and provide it with a semantics based on the epistemic state transition model. We then demonstrate how to use the language to represent the rules of an imperfect information game and formalize common game properties as well as epistemic properties. We also show how to use the framework to reason about players' own and each others' knowledge during game playing. Furthermore, we prove that the model-checking problem of the framework is in ${\mathrm{\Delta }}_2^P$, even though its lower bound is ${\mathrm{\Theta }}_2^P$. These results indicate that the framework makes a good balance between expressive power and computational efficiency. Finally we provide a sound and complete axiomatic system for this logic. With action, temporal and epistemic operators, the completeness proof requires a novel combination of techniques used for completeness of dynamic logic and epistemic temporal logics. The proof theory provides a feasible tool to analyze properties of a family of games.

本文提出了一个用于表示和推理不完善信息游戏的逻辑框架。我们首先使用标准的认知运算符扩展游戏描述语言（GDL），并为其提供基于认知状态转换模型的语义。然后，我们演示如何使用该语言来表示不完善的信息游戏的规则，并规范化常见游戏属性以及认知属性。我们还将展示如何使用该框架来推理游戏过程中玩家自身和彼此的知识。此外，我们证明该框架的模型检查问题在${\mathrm{\Delta }}_2^P$，即使其下限是 ${\mathrm{\Theta }}_2^P$。这些结果表明该框架在表达能力和计算效率之间取得了很好的平衡。最后，我们为该逻辑提供了一个完善的公理系统。对于动作，时间和认知运算符，完整性证明需要动态逻辑和认知时间逻辑的完整性的新颖组合。证明理论为分析游戏家族的性质提供了一种可行的工具。