The logical semantics of normal logic programs has traditionally been based on the notions of Clark's completion and two-valued or three-valued canonical models, including supported, stable, regular, and well-founded models. Two-valued interpretations can also be seen as states evolving under a program's update operator, producing a transition graph whose fixed points and cycles capture stable and oscillatory behaviors, respectively. We refer to this view as dynamical semantics since it characterizes the program's meaning in terms of state-space trajectories, as first introduced in the stable (supported) class semantics. Recently, we have established a formal connection between Datalog^\neg programs (i.e., normal logic programs without function symbols) and Boolean networks, leading to the introduction of the trap space concept for Datalog^\neg programs. In this paper, we generalize the trap space concept to arbitrary normal logic programs, introducing trap space semantics as a new approach to their interpretation. This new semantics admits both model-theoretic and dynamical characterizations, providing a comprehensive approach to understanding program behavior. We establish the foundational properties of the trap space semantics and systematically relate it to the established model-theoretic semantics, including the stable (supported), stable (supported) partial, regular, and L-stable model semantics, as well as to the dynamical stable (supported) class semantics. Our results demonstrate that the trap space semantics offers a unified and precise framework for proving the existence of supported classes, strict stable (supported) classes, and regular models, in addition to uncovering and formalizing deeper relationships among the existing semantics of normal logic programs.

翻译：正规逻辑程序的逻辑语义传统上基于Clark完备化以及二值或三值典范模型的概念，包括支持模型、稳定模型、正则模型和良基模型。二值解释亦可视为在程序更新算子作用下演化的状态，由此产生的转移图的定点与循环分别捕捉了稳定与振荡行为。我们将这一视角称为动态语义，因其通过状态空间轨迹来刻画程序意义，这一方法最初在稳定（支持）类语义中被引入。近期，我们建立了Datalog^\neg程序（即无函数符号的正规逻辑程序）与布尔网络之间的形式化关联，从而为Datalog^\neg程序引入了陷阱空间概念。本文中，我们将陷阱空间概念推广至任意正规逻辑程序，提出陷阱空间语义作为程序解释的新方法。该新语义兼具模型论与动态特征的表征能力，为理解程序行为提供了综合性框架。我们建立了陷阱空间语义的基础性质，并系统性地将其与既有模型论语义（包括稳定（支持）模型、稳定（支持）偏模型、正则模型及L-稳定模型语义）以及动态稳定（支持）类语义相关联。研究结果表明，陷阱空间语义为证明支持类、严格稳定（支持）类及正则模型的存在性提供了统一而精确的框架，同时揭示并形式化了正规逻辑程序现有语义之间更深层次的联系。