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50
Logic Programming and Negation: A Survey
 JOURNAL OF LOGIC PROGRAMMING
, 1994
"... We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the prooftheoretic and modeltheoretic issues and the relationships between them. ..."
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Cited by 245 (8 self)
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We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the prooftheoretic and modeltheoretic issues and the relationships between them.
Logic Programming and Knowledge Representation
 Journal of Logic Programming
, 1994
"... In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and sh ..."
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Cited by 224 (21 self)
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In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and show how each of the added features extends the representational power of the language.
Stable Semantics for Disjunctive Programs
 New Generation Computing
, 1991
"... We introduce the stable model semantics for disjunctive logic programs and deductive databases, which generalizes the stable model semantics, defined earlier for normal (i.e., nondisjunctive) programs. Depending on whether only total (2valued) or all partial (3valued) models are used we obtain th ..."
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Cited by 163 (2 self)
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We introduce the stable model semantics for disjunctive logic programs and deductive databases, which generalizes the stable model semantics, defined earlier for normal (i.e., nondisjunctive) programs. Depending on whether only total (2valued) or all partial (3valued) models are used we obtain the disjunctive stable semantics or the partial disjunctive stable semantics, respectively. The proposed semantics are shown to have the following properties: ffl For normal programs, the disjunctive (respectively, partial disjunctive) stable semantics coincides with the stable (respectively, partial stable) semantics. ffl For normal programs, the partial disjunctive stable semantics also coincides with the wellfounded semantics. ffl For locally stratified disjunctive programs both (total and partial) disjunctive stable semantics coincide with the perfect model semantics. ffl The partial disjunctive stable semantics can be generalized to the class of all disjunctive logic programs. ffl B...
WellFounded Semantics Coincides with ThreeValued Stable Semantics
 Fundamenta Informaticae
, 1990
"... We introduce 3valued stable models which are a natural generalization of standard (2valued) stable models. We show that every logic program P has at least one 3valued stable model and that the wellfounded model of any program P [VGRS90] coincides with the smallest 3valued stable model of P. We c ..."
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Cited by 139 (17 self)
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We introduce 3valued stable models which are a natural generalization of standard (2valued) stable models. We show that every logic program P has at least one 3valued stable model and that the wellfounded model of any program P [VGRS90] coincides with the smallest 3valued stable model of P. We conclude that the wellfounded semantics of an arbitrary logic program coincides with the 3valued stable model semantics. The 3valued stable semantics is closely related to nonmonotonic formalisms in AI. Namely, every program P can be translated into a suitable autoepistemic (resp. default) theory P so that the 3valued stable semantics of P coincides with the (3valued) autoepistemic (resp. default) semantics of P . Similar results hold for circumscription and CWA. Moreover, it can be shown that the 3valued stable semantics has a natural extension to the class of all disjunctive logic programs and deductive databases. The author acknowledges support from the National Science Foundat...
Preferred Answer Sets for Extended Logic Programs
 ARTIFICIAL INTELLIGENCE
, 1998
"... In this paper, we address the issue of how Gelfond and Lifschitz's answer set semantics for extended logic programs can be suitably modified to handle prioritized programs. In such programs an ordering on the program rules is used to express preferences. We show how this ordering can be used to de ..."
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Cited by 132 (17 self)
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In this paper, we address the issue of how Gelfond and Lifschitz's answer set semantics for extended logic programs can be suitably modified to handle prioritized programs. In such programs an ordering on the program rules is used to express preferences. We show how this ordering can be used to define preferred answer sets and thus to increase the set of consequences of a program. We define a strong and a weak notion of preferred answer sets. The first takes preferences more seriously, while the second guarantees the existence of a preferred answer set for programs possessing at least one answer set. Adding priorities
Well Founded Semantics for Logic Programs with Explicit Negation
 EUROPEAN CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 1992
"... The aim of this paper is to provide a semantics for general logic programs (with negation by default) extended with explicit negation, subsuming well founded semantics [22]. The Well Founded semantics for extended logic programs (WFSX) is expressible by a default theory semantics we have devised [11 ..."
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Cited by 122 (54 self)
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The aim of this paper is to provide a semantics for general logic programs (with negation by default) extended with explicit negation, subsuming well founded semantics [22]. The Well Founded semantics for extended logic programs (WFSX) is expressible by a default theory semantics we have devised [11]. This relationship improves the crossfertilization between logic programs and default theories, since we generalize previous results concerning their relationship [3, 4, 7, 1, 2], and there is an increasing use of logic programming with explicit negation for nonmonotonic reasoning [7, 15, 16, 13, 23]. It also clarifies the meaning of logic programs combining both explicit negation and negation by default. In particular, it shows that explicit negation corresponds exactly to classical negation in the default theory, and elucidates the use of rules in logic programs. Like defaults, rules are unidirectional, so their contrapositives are not implicit; the rule connective, /, is not materi...
On the Computational Cost of Disjunctive Logic Programming: Propositional Case
, 1995
"... This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of wellknown semantics, as well as the complexity of deciding whethe ..."
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Cited by 114 (26 self)
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This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of wellknown semantics, as well as the complexity of deciding whether a propositional formula is satised by all models according to a given semantics. We concentrate on nite propositional disjunctive programs with as wells as without integrity constraints, i.e., clauses with empty heads; the problems are located in appropriate slots of the polynomial hierarchy. In particular, we show that the consistency check is P 2 complete for the disjunctive stable model semantics (in the total as well as partial version), the iterated closed world assumption, and the perfect model semantics, and we show that the inference problem for these semantics is P 2 complete; analogous results are derived for the an
Dualities between Alternative Semantics for Logic Programming and Nonmonotonic Reasoning
 Journal of Automated Reasoning
, 1998
"... The GelfondLifschitz operator [GL88] associated with a logic program (and likewise the operator associated with default theories by Reiter) exhibits oscillating behavior. In the case of logic programs, there is always at least one finite, nonempty collection of Herbrand interpretations around whic ..."
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Cited by 87 (8 self)
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The GelfondLifschitz operator [GL88] associated with a logic program (and likewise the operator associated with default theories by Reiter) exhibits oscillating behavior. In the case of logic programs, there is always at least one finite, nonempty collection of Herbrand interpretations around which the GelfondLifschitz [GL88] operator "bounces around". The same phenomenon occurs with default logic when Reiter's operator \Gamma \Delta is considered. Based on this, a "stable class" semantics and "extension class" semantics was proposed in [BS90]. The main advantage of this semantics was that it was defined for all logic programs (and default theories), and that this definition was modelled using the standard operators existing in the literature such as Reiter's \Gamma \Delta operator. In this paper, our primary aim is to prove that there is a very interesting duality between stable class theory and the well founded semantics for logic programming. In the stable class semantics, class...
Logic Programming and Knowledge Representation  the AProlog perspective
 Artificial Intelligence
, 2002
"... In this paper we give a short introduction to logic programming approach to knowledge representation and reasoning. The intention is to help the reader to develop a 'feel' for the field's history and some of its recent developments. The discussion is mainly limited to logic programs under the answer ..."
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Cited by 87 (0 self)
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In this paper we give a short introduction to logic programming approach to knowledge representation and reasoning. The intention is to help the reader to develop a 'feel' for the field's history and some of its recent developments. The discussion is mainly limited to logic programs under the answer set semantics. For understanding of approaches to logic programming build on wellfounded semantics, general theories of argumentation, abductive reasoning, etc., the reader is referred to other publications.