Classical planning representation languages based on first-order logic have been extensively used to model and solve planning problems, but they struggle to capture implicit preconditions and effects that arise in complex planning scenarios. To address this problem, we propose an alternative approach to representing and transforming world states during planning. Based on the category-theoretic concepts of $\mathsf{C}$-sets and double-pushout rewriting (DPO), our proposed representation can effectively handle structured knowledge about world states that support domain abstractions at all levels. It formalizes the semantics of predicates according to a user-provided ontology and preserves the semantics when transitioning between world states. This method provides a formal semantics for using knowledge graphs and relational databases to model world states and updates in planning. In this paper, we compare our category-theoretic representation with the classical planning representation. We show that our proposed representation has advantages over the classical representation in terms of handling implicit preconditions and effects, and provides a more structured framework in which to model and solve planning problems.

翻译：经典规划表示语言基于一阶逻辑，已广泛应用于规划问题的建模与求解，但在捕捉复杂规划场景中的隐式前提条件和效果方面存在不足。针对这一问题，我们提出了一种替代方法来表征和转换规划过程中的世界状态。基于$\mathsf{C}$-集与双推重写（DPO）的范畴论概念，所提出的表示方法能够有效处理支持各层级领域抽象的世界状态结构化知识。该方法根据用户提供的本体形式化谓词语义，并在世界状态转换过程中保持语义一致性，为使用知识图谱和关系数据库建模规划中的世界状态与更新提供了形式化语义基础。本文通过比较范畴论表示与经典规划表示，论证了所提表示方法在处理隐式前提条件和效果方面优于经典表示，并为规划问题的建模与求解提供了更具结构化的框架。