摘要翻译：
本文给出了两种定义任意类型抽象约束原子（C原子）的逻辑程序答案集的方法。这些方法将常规逻辑程序的基于不动点和基于层次映射的回答集语义推广到具有任意类型C原子的逻辑程序。结果是四种不同的答案集定义，当应用于正常逻辑程序时是等价的。基于标准不动点的逻辑程序语义在两个方向上进行了推广，称为约简的答案集和补码的答案集。这些定义在处理否定为失败(naf)原子时各不相同，它们利用一个直接结果算子来执行答案集检查，该算子的定义依赖于C-原子W.R.T.的条件满足概念。一对解释。另外两个定义，称为强和弱良好支持模型，是正规逻辑程序的良好支持模型概念对C原子程序情形的推广。至于基于不动点语义的情况，这两种定义之间的差异根源于naf原子的处理。证明了约简（即补）答案集等价于程序的弱（即强）好支撑模型，从而将正规逻辑程序的稳定模型与好支撑模型的对应定理推广到含C原子的程序类。我们证明了新定义的语义与以前引入的单调C原子逻辑程序的语义是一致的，它们扩展了常规逻辑程序的原答案集语义。我们还研究了含C原子的程序回答集的一些性质，并将我们的定义与文献中的几种带集合的逻辑程序的语义联系起来。
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英文标题：
《Answer Sets for Logic Programs with Arbitrary Abstract Constraint Atoms》
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作者：
E. Pontelli, T. C. Son, P. H. Tu
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最新提交年份：
2011
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要：
  In this paper, we present two alternative approaches to defining answer sets for logic programs with arbitrary types of abstract constraint atoms (c-atoms). These approaches generalize the fixpoint-based and the level mapping based answer set semantics of normal logic programs to the case of logic programs with arbitrary types of c-atoms. The results are four different answer set definitions which are equivalent when applied to normal logic programs. The standard fixpoint-based semantics of logic programs is generalized in two directions, called answer set by reduct and answer set by complement. These definitions, which differ from each other in the treatment of negation-as-failure (naf) atoms, make use of an immediate consequence operator to perform answer set checking, whose definition relies on the notion of conditional satisfaction of c-atoms w.r.t. a pair of interpretations. The other two definitions, called strongly and weakly well-supported models, are generalizations of the notion of well-supported models of normal logic programs to the case of programs with c-atoms. As for the case of fixpoint-based semantics, the difference between these two definitions is rooted in the treatment of naf atoms. We prove that answer sets by reduct (resp. by complement) are equivalent to weakly (resp. strongly) well-supported models of a program, thus generalizing the theorem on the correspondence between stable models and well-supported models of a normal logic program to the class of programs with c-atoms. We show that the newly defined semantics coincide with previously introduced semantics for logic programs with monotone c-atoms, and they extend the original answer set semantics of normal logic programs. We also study some properties of answer sets of programs with c-atoms, and relate our definitions to several semantics for logic programs with aggregates presented in the literature.
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PDF链接：
https://arxiv.org/pdf/1110.2205