FLP answer set semantics without circular justifications for general logic programs

ISCAS OpenIR

	FLP answer set semantics without circular justifications for general logic programs
	Shen, Yi-Dong (1); Wang, Kewen (2); Eiter, Thomas (3); Fink, Michael (3); Redl, Christoph (3); Krennwallner, Thomas (3); Deng, Jun (1); Shen, Y.-D.(ydshen@ios.ac.cn)
	2014
发表期刊	Artificial Intelligence
ISSN	43702
卷号	213 页码:1-41
摘要	The answer set semantics presented by Faber et al. [27] has been widely used to define so called FLP answer sets for different types of logic programs. However, it was recently observed that when being extended from normal to more general classes of logic programs, this approach may produce answer sets with circular justifications that are caused by self-supporting loops. The main reason for this behavior is that the FLP answer set semantics is not fully constructive by a bottom up construction of answer sets. In this paper, we overcome this problem by enhancing the FLP answer set semantics with a level mapping formalism such that every answer set I can be built by fixpoint iteration of a one-step provability operator (more precisely, an extended van Emden-Kowalski operator for the FLP reduct f^ΠI). This is inspired by the fact that under the standard answer set semantics, each answer set I of a normal logic program Π is obtainable by fixpoint iteration of the standard van Emden-Kowalski one-step provability operator for the Gelfond-Lifschitz reduct ^ΠI, which induces a level mapping. The enhanced FLP answer sets, which we call well-justified FLP answer sets, are thanks to the level mapping free of circular justifications. As a general framework, the well-justified FLP answer set semantics applies to logic programs with first-order formulas, logic programs with aggregates, description logic programs, hex-programs etc., provided that the rule satisfaction is properly extended to such general logic programs. We study in depth the computational complexity of FLP and well-justified FLP answer sets for general classes of logic programs. Our results show that the level mapping does not increase the worst-case complexity of FLP answer sets. Furthermore, we describe an implementation of the well-justified FLP answer set semantics, and report about an experimental evaluation, which indicates a potential for performance improvements by the level mapping in practice. © 2014 The Authors.; The answer set semantics presented by Faber et al. [27] has been widely used to define so called FLP answer sets for different types of logic programs. However, it was recently observed that when being extended from normal to more general classes of logic programs, this approach may produce answer sets with circular justifications that are caused by self-supporting loops. The main reason for this behavior is that the FLP answer set semantics is not fully constructive by a bottom up construction of answer sets. In this paper, we overcome this problem by enhancing the FLP answer set semantics with a level mapping formalism such that every answer set I can be built by fixpoint iteration of a one-step provability operator (more precisely, an extended van Emden-Kowalski operator for the FLP reduct f^ΠI). This is inspired by the fact that under the standard answer set semantics, each answer set I of a normal logic program Π is obtainable by fixpoint iteration of the standard van Emden-Kowalski one-step provability operator for the Gelfond-Lifschitz reduct ^ΠI, which induces a level mapping. The enhanced FLP answer sets, which we call well-justified FLP answer sets, are thanks to the level mapping free of circular justifications. As a general framework, the well-justified FLP answer set semantics applies to logic programs with first-order formulas, logic programs with aggregates, description logic programs, hex-programs etc., provided that the rule satisfaction is properly extended to such general logic programs. We study in depth the computational complexity of FLP and well-justified FLP answer sets for general classes of logic programs. Our results show that the level mapping does not increase the worst-case complexity of FLP answer sets. Furthermore, we describe an implementation of the well-justified FLP answer set semantics, and report about an experimental evaluation, which indicates a potential for performance improvements by the level mapping in practice. © 2014 The Authors.
收录类别	SCI ; EI
关键词	Answer Set Programming Knowledge Representation Nonmonotonic Reasoning Logic Programs With First-order Formulas Level Mappings Circular Justifications
部门归属	(1) State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China; (2) School of Computing and Information Technology, Griffith University, Brisbane, QLD 4111, Australia; (3) Institut für Informationssysteme, Technische Universität Wien, Favoritenstrasse 9-11, A-1040 Vienna, Austria
语种	英语
WOS记录号	WOS:000337772500001
引用统计	被引频次：27[WOS] [WOS记录] [WOS相关记录]
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/16844
专题	中国科学院软件研究所
通讯作者	Shen, Y.-D.(ydshen@ios.ac.cn)
推荐引用方式 GB/T 7714	Shen, Yi-Dong ,Wang, Kewen ,Eiter, Thomas ,et al. FLP answer set semantics without circular justifications for general logic programs[J]. Artificial Intelligence,2014,213:1-41.
APA	Shen, Yi-Dong .,Wang, Kewen .,Eiter, Thomas .,Fink, Michael .,Redl, Christoph .,...&Shen, Y.-D..(2014).FLP answer set semantics without circular justifications for general logic programs.Artificial Intelligence,213,1-41.
MLA	Shen, Yi-Dong ,et al."FLP answer set semantics without circular justifications for general logic programs".Artificial Intelligence 213(2014):1-41.