Title: FLP answer set semantics without circular justifications for general logic programs

Author: Shen, Yi-Dong (1)
; Wang, Kewen (2)
; Eiter, Thomas (3)
; Fink, Michael (3)
; Redl, Christoph (3)
; Krennwallner, Thomas (3)
; Deng, Jun (1)
Corresponding Author: Shen, Y.-D.(ydshen@ios.ac.cn)
Keyword: Answer set programming
; Knowledge representation
; Nonmonotonic reasoning
; Logic programs with first-order formulas
; Level mappings
; Circular justifications
Source: Artificial Intelligence
Issued Date: 2014
Volume: 213, Pages: 1-41 Indexed Type: SCI
; EI
Department: (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
Abstract: 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.
English Abstract: 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.
Language: 英语
WOS ID: WOS:000337772500001
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Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/16844
Appears in Collections: 软件所图书馆_期刊论文

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Recommended Citation:
Shen, Yi-Dong ,Wang, Kewen ,Eiter, Thomas ,et al. FLP answer set semantics without circular justifications for general logic programs[J]. Artificial Intelligence,2014-01-01,213:1-41.