Automated planning in AI and the logics of knowing how have close connections. In the recent literature, various planning-based know-how logics have been proposed and studied, making use of several notions of planning in AI. In this paper, we explore the reverse direction by using a multi-agent logic of knowing how to do know-how-based planning via model checking and theorem proving/satisfiability checking. Based on our logical framework, we propose two new classes of related planning problems: higher-order epistemic planning and meta-level epistemic planning, which generalize the current genre of epistemic planning in the literature. The former is for planning about planning, i.e., planning with higher-order goals that are again about epistemic planning, e.g., finding a plan for an agent to make sure p such that the adversary does not know how to make p false in the future. The latter is about planning at the meta-level by abstract reasoning combining knowledge-how from different agents, e.g., given that i knows how to prove a lemma and i knows j knows how to prove the theorem once the lemma is proved, we should derive that i knows how to let j knows how to prove the theorem. To make these possible, our framework features not only the operators of know-that and know-how but also a temporal operator □, which can help in capturing both the local and global knowledge-how. We axiomatize this powerful logic over finite models with perfect recall and show its decidability. We also give a PTIME algorithm for the model checking problem over finite models.

中文翻译：

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知道如何规划规划：高阶和元层次的认识规划


AI 中的自动规划和 knowing how 的逻辑有着密切的联系。在最近的文献中，利用人工智能中的几个规划概念，提出了并研究了各种基于规划的专有技术逻辑。在本文中，我们通过使用多智能体逻辑来探索相反的方向，即知道如何通过模型检查和定理证明/满足性检查来进行基于专有技术的规划。基于我们的逻辑框架，我们提出了两类新的相关规划问题：高阶认知规划和元层次认知规划，它们概括了当前文献中的认识规划类型。前者是关于规划的规划，即具有更高阶目标的规划，这些目标又是关于认知规划的，例如，为代理找到一个计划来确保 p，这样对手就不知道将来如何使 p 成为假的。后者是关于通过抽象推理结合来自不同主体的知识在元层面进行规划，例如，假设 i 知道如何证明引理，我知道 j 知道如何证明定理一旦引理被证明，我们应该推导出 i 知道如何让 j 知道如何证明定理。为了实现这些，我们的框架不仅具有 know-that 和 know-how 的运算符，还具有时间运算符 □，这有助于捕获本地和全局知识。我们在有限模型上公理化了这个强大的逻辑，并完美地召回并展示了它的可判定性。我们还为有限模型上的模型检查问题提供了一个 PTIME 算法。