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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 242 (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.
The Family of Stable Models
, 1993
"... The family of all stable models for a logic program has a surprisingly simple overall structure, once two naturally occurring orderings are made explicit. In a socalled knowledge ordering based on degree of definedness, every logic program P has a smallest stable model, s k P it is the well ..."
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Cited by 64 (4 self)
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The family of all stable models for a logic program has a surprisingly simple overall structure, once two naturally occurring orderings are made explicit. In a socalled knowledge ordering based on degree of definedness, every logic program P has a smallest stable model, s k P it is the wellfounded model. There is also a dual largest stable model, S k P , which has not been considered before. There is another ordering based on degree of truth. Taking the meet and the join, in the truth ordering, of the two extreme stable models s k P and S k P just mentioned, yields the alternating fixed points of [29], denoted s t P and S t P here. From s t P and S t P in turn, s k P and S k P can be produced again, using the meet and join of the knowledge ordering. All stable models are bounded by these four valuations. Further, the methods of proof apply not just to logic programs considered classically, but to logic programs over any bilattice meeting certain co...
A Survey of Paraconsistent Semantics for Logic Programs
 HANDBOOK OF DEFEASIBLE REASONING AND UNCERTAINTY MANAGEMENT SYSTEMS
, 1998
"... In this chapter we motivate the use of paraconsistency, and survey the most salient paraconsistent semantics for (extended) logic programs, which are briefly defined and explained. Most of the semantics are accompanied with their multivalued model theory, giving them a new perspective. The surv ..."
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Cited by 36 (9 self)
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In this chapter we motivate the use of paraconsistency, and survey the most salient paraconsistent semantics for (extended) logic programs, which are briefly defined and explained. Most of the semantics are accompanied with their multivalued model theory, giving them a new perspective. The survey also presents new results regarding the embedding of part of these semantics into normal logic programs under WellFounded Semantics [20], Partial Stable Model Semantics (or stationary semantics) [48], and Stable Model Semantics [21]. Furthermore, a concise recapitulation of other related paraconsistent formalisms is made. The reader is assumed to have a good knowledge of the semantics of normal logic programs. We believe a comprehensive coverage of the topic as it stands at present is attained here.
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 28 (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...
A uniform approach to logic programming semantics
 Theory and Practice of Logic Programming
, 2005
"... ..."
Computing and Comparing Semantics of Programs in Fourvalued Logics
 IN PROC. MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE (MFCS'99), NUMBER 1672 IN LNCS
, 1999
"... The different semantics that can be assigned to a logic program correspond to different assumptions made concerning the atoms whose logical values cannot be inferred from the rules. Thus, the well founded semantics corresponds to the assumption that every such atom is false, while the KripkeKleene ..."
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Cited by 7 (3 self)
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The different semantics that can be assigned to a logic program correspond to different assumptions made concerning the atoms whose logical values cannot be inferred from the rules. Thus, the well founded semantics corresponds to the assumption that every such atom is false, while the KripkeKleene semantics corresponds to the assumption that every such atom is unknown. In this paper, we propose to unify and extend this assumptionbased approach by introducing parameterized semantics for logic programs. The parameter holds the value that one assumes for all atoms whose logical values cannot be inferred from the rules. We work within Belnap's fourvalued logic, and we consider the class of logic programs defined by Fitting. Following Fitting's approach, we define a simple operator that allows us to compute the parameterized semantics, and to compare and combine semantics obtained for different values of the parameter. The semantics proposed by Fitting corresponds to the value false. We also show that our approach captures and extends the usual semantics of conventional logic programs thereby unifying their computation.
ManyValued NonMonotonic Modal Logics
, 1992
"... Among nonmonotonic systems of reasoning, nonmonotonic modal logics, and autoepistemic logic in particular, have had considerable success. The presence of explicit modal operators allows flexibility in the embedding of other approaches. Also several theoretical results of interest have been establi ..."
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Cited by 6 (2 self)
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Among nonmonotonic systems of reasoning, nonmonotonic modal logics, and autoepistemic logic in particular, have had considerable success. The presence of explicit modal operators allows flexibility in the embedding of other approaches. Also several theoretical results of interest have been established concerning these logics. In this paper we introduce nonmonotonic modal logics based on manyvalued logics, rather than on classical logic. This extends earlier work of ours on manyvalued modal logics. Intended applications are to situations involving several reasoners, not just one as in the standard development. 1 Introduction Several kinds of nonmonotonic logics have been considered over the past dozen years. Among these, nonmonotonic modal logics have been particularly interesting. These, of course, have explicitly occurring modal operators, and this allows for fine control when translating from other formalisms; see [13, 5], for instance. Following the ideas of McDermott and Do...
A Paraconsistent Semantics With Contradiction Support Detection
"... We begin by motivating the use of paraconsistency and the detection of contradiction supported conclusions by recourse to examples. Next we overview WFSX p and present its embedding into WFS. We then address the problem of detecting contradiction support and relate it to WFSX p's intrinsic pr ..."
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Cited by 5 (1 self)
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We begin by motivating the use of paraconsistency and the detection of contradiction supported conclusions by recourse to examples. Next we overview WFSX p and present its embedding into WFS. We then address the problem of detecting contradiction support and relate it to WFSX p's intrinsic properties. Afterwards, we show how to implement two recent modal contradiction related constructs in the language of extended logic programs in order to gain explicit control of contradiction propagation. We finish by making comparisons and drawing some conclusions.
Canonical Kripke Models and The Intuitionistic Semantics of Logic Programs (Extended Abstract)
, 1993
"... ) Fangqing Dong and Laks V.S. Lakshmanan Department of Computer Science Concordia University Montreal, Quebec, Canada H3G 1M8 Abstract Motivated by the problem of extending stable semantics (SS) and wellfounded semantics (WFS) while avoiding their drawbacks, we propose a new simple and intuitive s ..."
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) Fangqing Dong and Laks V.S. Lakshmanan Department of Computer Science Concordia University Montreal, Quebec, Canada H3G 1M8 Abstract Motivated by the problem of extending stable semantics (SS) and wellfounded semantics (WFS) while avoiding their drawbacks, we propose a new simple and intuitive semantics for (normal) logic programs, called canonical Kripke model semantics. Our approach is based on formulating stability in an intuitionistic framework which helps us overcome several drawbacks. As a consequence, every normal program has a unique "intended" canonical Kripke model. The canonical Kripke model semantics is a proper extension of SS and WFS, and it avoids the drawbacks associated with SS and WFS. The canonical Kripke model of a normal program exactly captures the 3valued autoepistemic consequences of the associated AE theory, and can be obtained as the greatest fixpoint of a deflationary operator KP defined on Kripke structures. 1 Introduction The fields of nonmonotonic ...