Answer Set Programming (ASP) is a prominent rule-based language for knowledge representation and reasoning with roots in logic programming and non-monotonic reasoning. The aim to capture the essence of removing (ir)relevant details in ASP programs led to the investigation of different notions, from strong persistence (SP) forgetting, to faithful abstractions, and, recently, strong simplifications, where the latter two can be seen as relaxed and strengthened notions of forgetting, respectively. Although it was observed that these notions are related, especially given that they have characterizations through the semantics for strong equivalence, it remained unclear whether they can be brought together. In this work, we bridge this gap by introducing a novel relativized equivalence notion, which is a relaxation of the recent simplification notion, that is able to capture all related notions from the literature. We provide necessary and sufficient conditions for relativized simplifiability, which shows that the challenging part is for when the context programs do not contain all the atoms to remove. We then introduce an operator that combines projection and a relaxation of (SP)-forgetting to obtain the relativized simplifications. We furthermore present complexity results that complete the overall picture.

翻译：回答集编程(ASP)是一种基于规则的显式知识表示与推理语言，根植于逻辑编程和非单调推理。为捕捉从ASP程序中移除(不)相关细节的本质，研究者先后提出了从强持久(SP)遗忘、忠实抽象到近期强简化等不同概念——后两者可分别视为遗忘概念的松弛与强化形式。尽管已有研究指出这些概念存在关联（尤其它们都可通过对强等价的语义刻画实现），但尚不清楚它们能否被统一。本研究通过引入一种新颖的相对化等价概念弥补了这一空白，该概念是近期简化概念的松弛形式，能够统一涵盖文献中所有相关概念。我们给出了相对化可简化性的充分必要条件，揭示了核心难点在于上下文程序未包含全部待移除原子时的情形。随后引入将投影与(SP)遗忘松弛化相结合的操作符以实现相对化简化，并进一步给出了复杂度结果以完善整体图景。