Negation by default and unstratifiable logic programs

Bidoit, Nicole; Froidevaux, Christine

doi:10.1016/0304-3975(51)90004-7

Cited by 84 publications

(48 citation statements)

References 12 publications

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“…Testing 1 ≡ 2 is well-known to be co-NP. This result per se follows directly from[3] and[26], who showed that deciding whether an answer set exists for a program is NP-complete, but was, to the best of our knowledge, reported formally only recently in Theorem 6.17 of[17] in the context of more complex settings.…”

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confidence: 83%

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Strong order equivalence

Faber

Konczak

2006

Ann Math Artif Intell

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Recently, strong equivalence for Answer Set Programming has been studied intensively, and was shown to be beneficial for modular programming and automated optimization. In this paper we define the novel notion of strong order equivalence for logic programs with preferences (ordered logic programs). Based on this definition we give, for several semantics for preference handling, necessary and sufficient conditions for programs to be strongly order equivalent. These results allow us also to associate a so-called SOE structure to each ordered logic program, such that two ordered logic programs are strongly order equivalent if and only if their SOE structures coincide. We also present the relationships among the studied semantics with respect to strong order equivalence, which differs considerably from their relationships with respect to preferred answer sets. Furthermore, we study the computational complexity of several reasoning tasks associated to strong order equivalence. Finally, based on the obtained results, we present -for the first timesimplification methods for ordered logic programs. Mathematics Subject Classifications (2000)68T27 · 68T30 · 68T15

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confidence: 83%

“…Let φ = C 1 ∧ · · · ∧ C n be a 3CNF, i.e. a conjunction of clauses n i=1 L i,1 ∨ L i,2 ∨ L i, 3 where the L i, j are classical literals over propositional atoms X = {x 1 , . .…”

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confidence: 99%

Strong order equivalence

Faber

Konczak

2006

Ann Math Artif Intell

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“…The correspondence between Reiter's default logic [16] and logic programming has been exhaustively studied ( [2], [3], [8]) this section discusses the relation between the variant of default logic proposed by Łukaszewicz and justified answer sets of logic programs. The definition of justified extensions in [13] is based on fixed-points.…”

Section: Vmentioning

confidence: 99%

Justified Answer Set Programming

Hassan¹

2012

IOSRJCE

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“…It is its perfect model. It turns out that stable models of general logic programs are closely connected with Default Logic, Bidoit and Froidevaux, [55],…”

Section: Stable Modelsmentioning

confidence: 99%