Negation as failure in the head

Inoue, Katsumi; Sakama, Chiaki

doi:10.1016/s0743-1066(97)10001-2

Cited by 81 publications

(65 citation statements)

References 26 publications

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“…This requirement of consistency is implicit in Prop. 16 with the precondition that C 0 is a conjunctive clause.…”

Section: Example 17 (Prime Implicants Form With Partial Stable Models)mentioning

confidence: 99%

“…As noted in [25], a major drawback of this method is that it involves the actual computation of all explanations, not taking into account that the minimal ones provide a succinct representation of them. A variant of [17] is described in [16], where a generalization of the stable model semantics to rules with literals instead of just atoms, as well as disjunctive heads and negation as failure in the head is considered. Computation of explanations is there encoded similarly to [17], except that the openness of abducibles p is expressed by rules (p | not p ).…”

Section: Related Workmentioning

confidence: 99%

“…Computation of explanations is there encoded similarly to [17], except that the openness of abducibles p is expressed by rules (p | not p ). Minimality with respect to the set of abducibles is taken into account [16,Corollary 3.3], but in a way that just suggests to compute first the models and only afterwards extract explanations and compare them with respect to minimality. In [25], the approach of [20] is improved by discerning redundant explanations.…”

Section: Related Workmentioning

confidence: 99%

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Abduction in Logic Programming as Second-Order Quantifier Elimination

Wernhard

2013

Frontiers of Combining Systems

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Abstract. It is known that skeptical abductive explanations with respect to classical logic can be characterized semantically in a natural way as formulas with second-order quantifiers. Computing explanations is then just elimination of the second-order quantifiers. By using application patterns and generalizations of second-order quantification, like literal projection, the globally weakest sufficient condition and circumscription, we transfer these principles in a unifying framework to abduction with three non-classical semantics of logic programming: stable model, partial stable model and well-founded semantics. New insights are revealed about abduction with the partial stable model semantics.

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“…This requirement of consistency is implicit in Prop. 16 with the precondition that C 0 is a conjunctive clause.…”

Section: Example 17 (Prime Implicants Form With Partial Stable Models)mentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Abduction in Logic Programming as Second-Order Quantifier Elimination

Wernhard

2013

Frontiers of Combining Systems

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“…If, in addition, M is a minimal hitting set of {hd (r) | r ∈ P and M |= bd(r)}, then M is a supported model of P (Brass & Dix 1997;Inoue & Sakama 1998). It is well known that M ⊆ At is a supported model of P if and only if M is a model of P and for every a ∈ M there is a rule r ∈ P such that M |= bd (r) and {a} = hd (r) ∩ M .…”

Section: Preliminariesmentioning

confidence: 99%

Hyperequivalence of logic programs with respect to supported models

Truszczyński

Woltran

2008

Ann Math Artif Intell

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Recent research in nonmonotonic logic programming has focused on certain types of program equivalence, which we refer to here as hyperequivalence, that are relevant for program optimization and modular programming. So far, most results concern hyperequivalence relative to the stable-model semantics. However, other semantics for logic programs are also of interest, especially the semantics of supported models which, when properly generalized, is closely related to the autoepistemic logic of Moore. In this paper, we consider a family of hyperequivalence relations for programs based on the semantics of supported and supported minimal models. We characterize these relations in model-theoretic terms. We use the characterizations to derive complexity results concerning testing whether two programs are hyperequivalent relative to supported and supported minimal models.

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“…Moreover, S is a minimal explanation (i.e. there is no explanation S ⊂ S) of G iff Γ ∪ {← not G} has a consistent A-minimal stable model M such that S = M ∩ A (Inoue & Sakama, 1998).…”

Section: Extended and Abductive Programsmentioning

confidence: 99%

On the Semantics of Logic Programs with Preferences

Greco

Trubitsyna

Zumpano

2006

Logics in Artificial Intelligence

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This work is a contribution to prioritized reasoning in logic programming in the presence of preference relations involving atoms. The technique, providing a new interpretation for prioritized logic programs, is inspired by the semantics of Prioritized Logic Programming and enriched with the use of structural information of preference of Answer Set Optimization Programming. Specifically, the analysis of the logic program is carried out together with the analysis of preferences in order to determine the choice order and the sets of comparable models. The new semantics is compared with other approaches known in the literature and complexity analysis is also performed, showing that, with respect to other similar approaches previously proposed, the complexity of computing preferred stable models does not increase.

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Negation as failure in the head

Cited by 81 publications

References 26 publications

Abduction in Logic Programming as Second-Order Quantifier Elimination

Abduction in Logic Programming as Second-Order Quantifier Elimination

Hyperequivalence of logic programs with respect to supported models

On the Semantics of Logic Programs with Preferences

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