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49
The WellFounded Semantics for General Logic Programs
 Journal of the ACM
, 1991
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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 268 (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 234 (20 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.
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 128 (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
Propositional Circumscription and Extended Closed World Reasoning are $\Pi^P_2$complete
 Theoretical Computer Science
, 1993
"... Circumscription and the closed world assumption with its variants are wellknown nonmonotonic techniques for reasoning with incomplete knowledge. Their complexity in the propositional case has been studied in detail for fragments of propositional logic. One open problem is whether the deduction prob ..."
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Cited by 106 (20 self)
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Circumscription and the closed world assumption with its variants are wellknown nonmonotonic techniques for reasoning with incomplete knowledge. Their complexity in the propositional case has been studied in detail for fragments of propositional logic. One open problem is whether the deduction problem for arbitrary propositional theories under the extended closed world assumption or under circumscription is $\Pi^P_2$complete, i.e., complete for a class of the second level of the polynomial hierarchy. We answer this question by proving these problems $\Pi^P_2$complete, and we show how this result applies to other variants of closed world reasoning.
Stationary Semantics for Normal and Disjunctive Logic Programs
 Annals of Mathematics and Artificial Intelligence
, 1991
"... this paper we show, however, that stationary expansions can be equivalently defined in terms of classical, 2valued logic. As a byproduct, we obtain a simpler and more natural description of stationary expansions. ..."
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Cited by 74 (15 self)
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this paper we show, however, that stationary expansions can be equivalently defined in terms of classical, 2valued logic. As a byproduct, we obtain a simpler and more natural description of stationary expansions.
A Procedural Semantics for Well Founded Negation in Logic Programs
 Journal of Logic programming
, 1989
"... We introduce global SLSresolution, a procedural semantics for wellfounded negation as defined by Van Gelder, Ross and Schlipf. Global SLSresolution extends Przymusinski 's SLSresolution, and may be applied to all programs, whether locally stratified or not. 1 Global SLSresolution is define ..."
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Cited by 60 (2 self)
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We introduce global SLSresolution, a procedural semantics for wellfounded negation as defined by Van Gelder, Ross and Schlipf. Global SLSresolution extends Przymusinski 's SLSresolution, and may be applied to all programs, whether locally stratified or not. 1 Global SLSresolution is defined in terms of global trees, a new data structure representing the dependence of goals on derived negative subgoals. We prove that global SLSresolution is sound with respect to the wellfounded semantics, and complete for nonfloundering queries. While not effective in general, global SLSresolution is effective for classes of "acyclic" programs, and can be augmented with a memoing device to be effective for all functionfree programs. This research was supported by the National Science Foundation under grant IRI8722886, by a grant from IBM Corporation, and by the United States Air Force Office of Scientific Research under contract AFOSR880266. A preliminary version of this paper was presen...
On Logic Program Semantics with Two Kinds of Negation
 Int. Joint Conf. and Symp. on LP
, 1992
"... Recently several authors have stressed and showed the importance of having a second kind of negation in logic programs for use in deductive databases, knowledge representation, and nonmonotonic reasoning [6, 7, 8, 9, 13, 14, 15, 24]. Different semantics for logic programs extended with :negation ( ..."
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Cited by 50 (16 self)
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Recently several authors have stressed and showed the importance of having a second kind of negation in logic programs for use in deductive databases, knowledge representation, and nonmonotonic reasoning [6, 7, 8, 9, 13, 14, 15, 24]. Different semantics for logic programs extended with :negation (extended logic programs) have appeared [1, 4, 6, 9, 11, 12, 17, 19, 24] but, contrary to what happens with semantics for normal logic programs, there is no general comparison among them, specially in what concerns the use and meaning of the newly introduced :negation. The goal of this paper is to contrast a variety of these semantics in what concerns their use and meaning of :negation, and its relation to classical negation and to the default negation of normal programs, here denoted by not : To this purpose we define a parametrizeable schema to encompass and characterize a diversity of proposed semantics for extended logic programs, where the parameters are two: one the axioms AX: defin...