一阶答案集编程中的非递归聚合公理化

IF 4.5 3区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Jorge Fandinno, Zachary Hansen, Yuliya Lierler
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引用次数: 0

摘要

本文对答案集编程理论基础的发展做出了贡献。Ferraris、Lee 和 Lifschitz 关于 SM 算子的开创性工作提出了逻辑(答案集)程序的定义/语义学,其基础是类似于并行周延的语法转换。该定义使用经典(二阶)逻辑,避免了对接地或固定点的引用,与前人的定义截然不同。然而,这项工作缺乏对关键且常用的答案集编程语言构造(称为聚合)的形式化。在本文中,我们基于 SM 算子的多排序广义化,提出了具有聚合的逻辑程序的表征。该表征为聚合运算和聚合元素引入了新的函数符号,通过为 SM 变换的结果添加适当的公理,可以固定其含义。我们证明,我们的表征与逻辑程序的 ASP-Core-2 语义相吻合,而且,如果我们允许通过聚合进行非正递归,它还与答案集求解器 CLINGO 的语义相吻合。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Axiomatization of Non-Recursive Aggregates in First-Order Answer Set Programming
This paper contributes to the development of theoretical foundations of answer set programming. Groundbreaking work on the SM operator by Ferraris, Lee, and Lifschitz proposed a definition/semantics for logic (answer set) programs based on a syntactic transformation similar to parallel circumscription. That definition radically differed from its predecessors by using classical (second-order) logic and avoiding reference to either grounding or fixpoints. Yet, the work lacked the formalization of crucial and commonly used answer set programming language constructs called aggregates. In this paper, we present a characterization of logic programs with aggregates based on a many-sorted generalization of the SM operator. This characterization introduces new function symbols for aggregate operations and aggregate elements, whose meaning can be fixed by adding appropriate axioms to the result of the SM transformation. We prove that our characterization coincides with the ASP-Core-2 semantics for logic programs and, if we allow non-positive recursion through aggregates, it coincides with the semantics of the answer set solver CLINGO.
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来源期刊
Journal of Artificial Intelligence Research
Journal of Artificial Intelligence Research 工程技术-计算机:人工智能
CiteScore
9.60
自引率
4.00%
发文量
98
审稿时长
4 months
期刊介绍: JAIR(ISSN 1076 - 9757) covers all areas of artificial intelligence (AI), publishing refereed research articles, survey articles, and technical notes. Established in 1993 as one of the first electronic scientific journals, JAIR is indexed by INSPEC, Science Citation Index, and MathSciNet. JAIR reviews papers within approximately three months of submission and publishes accepted articles on the internet immediately upon receiving the final versions. JAIR articles are published for free distribution on the internet by the AI Access Foundation, and for purchase in bound volumes by AAAI Press.
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