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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 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.
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...
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...
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 and Databases: a 20 Year Retrospective
, 1996
"... . At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire ..."
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Cited by 55 (1 self)
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. At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire and Nicolas in Toulouse, France, which culminated in a workshop held in Toulouse, France in 1977. It is appropriate, then to provide an assessment as to what has been achieved in the twenty years since the field started as a distinct discipline. In this retrospective I shall review developments that have taken place in the field, assess the contributions that have been made, consider the status of implementations of deductive databases and discuss the future of work in this area. 1 Introduction As described in [234], the use of logic and deduction in databases started in the late 1960s. Prominent among the developments was the work by Levien and Maron [202, 203, 199, 200, 201] and Kuhns [1...
Abduction from Logic Programs: Semantics and Complexity
 Theoretical Computer Science
, 1998
"... Abduction from observations and a theory, find using hypotheses an explanation for the observations  gained increasing interest during the last years. This form of reasoning has wide applicability in different areas of computer science; in particular, it has been recognized as an important pr ..."
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Cited by 37 (7 self)
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Abduction from observations and a theory, find using hypotheses an explanation for the observations  gained increasing interest during the last years. This form of reasoning has wide applicability in different areas of computer science; in particular, it has been recognized as an important principle of commonsense reasoning. In this paper, we define a general abduction model for logic programming, where the inference operator (i.e., the semantics to be applied on programs), can be specified by the user. Advanced forms of logic programming have been proposed as valuable tools for knowledge representation and reasoning. We show that logic programming semantics can be more meaningful for abductive reasoning than classical inference by providing examples from the area of knowledge representation and reasoning. The main part of the paper is devoted to an extensive study of the computational complexity of the principal problems in abductive reasoning, which are: Given an inst...
Knowledge Representation with Logic Programs
 DEPT. OF CS OF THE UNIVERSITY OF KOBLENZLANDAU
, 1996
"... In this tutorialoverview, which resulted from a lecture course given by the authors at ..."
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Cited by 31 (6 self)
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In this tutorialoverview, which resulted from a lecture course given by the authors at
An Overview of Nonmonotonic Reasoning and Logic Programming
 Journal of Logic Programming, Special Issue
, 1993
"... The focus of this paper is nonmonotonic reasoning as it relates to logic programming. I discuss the prehistory of nonmonotonic reasoning starting from approximately 1958. I then review the research that has been accomplished in the areas of circumscription, default theory, modal theories and logic ..."
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Cited by 27 (2 self)
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The focus of this paper is nonmonotonic reasoning as it relates to logic programming. I discuss the prehistory of nonmonotonic reasoning starting from approximately 1958. I then review the research that has been accomplished in the areas of circumscription, default theory, modal theories and logic programming. The overview includes the major results developed including complexity results that are known about the various theories. I then provide a summary which includes an assessment of the field and what must be done to further research in nonmonotonic reasoning and logic programming. 1 Introduction Classical logic has played a major role in computer science. It has been an important tool both for the development of architecture and of software. Logicians have contended that reasoning, as performed by humans, is also amenable to analysis using classical logic. However, workers in the field of artificial 1 This paper is an updated version of an invited Banquet Address, First Interna...