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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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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.
ThreeValued NonMonotonic Formalisms And Semantics of Logic Programs
 Artificial Intelligence
, 1991
"... We introduce 3valued extensions of major nonmonotonic formalisms and we prove that the recently proposed wellfounded semantics of logic programs is equivalent, for arbitrary logic programs, to 3valued forms of McCarthy's circumscription, Reiter's closed world assumption, Moore's a ..."
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Cited by 36 (6 self)
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We introduce 3valued extensions of major nonmonotonic formalisms and we prove that the recently proposed wellfounded semantics of logic programs is equivalent, for arbitrary logic programs, to 3valued forms of McCarthy's circumscription, Reiter's closed world assumption, Moore's autoepistemic logic and Reiter's default theory. This result not only provides a further justification of the wellfounded semantics, as a natural extension of the perfect model semantics from the class of stratified programs to the class of all logic programs, but it also establishes the class of all logic programs as a large class of theories, for which natural forms of all four nonmonotonic formalisms coincide. It also paves the way for using efficient computation methods, developed for logic programming, as inference mechanisms for nonmonotonic reasoning. 1 Introduction A precise meaning or semantics must be associated with any logic program or a deductive database in order to provide its declarative...
REVISE: An Extended Logic Programming System for Revising Knowledge Bases
 IN PROC. OF KR94
, 1994
"... In this paper we describe REVISE, an extended logic programming system for revising knowledge bases. REVISE is based on logic programming with explicit negation, plus a twovalued assumption revision to face contradiction , encompasses the notion of preference levels. Its reliance on logic programmi ..."
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Cited by 34 (24 self)
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In this paper we describe REVISE, an extended logic programming system for revising knowledge bases. REVISE is based on logic programming with explicit negation, plus a twovalued assumption revision to face contradiction , encompasses the notion of preference levels. Its reliance on logic programming allows efficient computation and declarativity, whilst its use of explicit negation, revision and preference levels enables modeling of a variety of problems including default reasoning, belief revision and modelbased reasoning. It has been implemented as a Prologmeta interpreter and tested on a spate of examples, namely the representation of diagnosis strategies in modelbased reasoning systems.
WellFounded and Stationary Models of Logic Programs
 ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE
, 1994
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Stationary Default Extensions
 Fundamenta Informaticae
, 1992
"... this paper we introduce the class of so called stationary extensions of a default theory. Stationary extensions include, as a special case, Reiter's original default extensions but allow us to eliminate their drawbacks that were mentioned above. Every default theory \Delta has at least one stat ..."
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Cited by 25 (0 self)
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this paper we introduce the class of so called stationary extensions of a default theory. Stationary extensions include, as a special case, Reiter's original default extensions but allow us to eliminate their drawbacks that were mentioned above. Every default theory \Delta has at least one stationary extension and among its extensions there always exists the least stationary extension E \Delta . The (cautious) stationary semantics S (\Delta) of a default theory \Delta, i.e., the theory consisting of sentences which are true in all stationary extensions of \Delta, is always welldefined, and, since it clearly coincides with the least stationary extension E \Delta of \Delta, it is itself a stationary extension of \Delta. The stationary semantics of default theories is always cumulatively monotonic and it can be computed by means of a natural iterative procedure. The complexity of its computation essentially coincides with the computational complexity of satisfiability tests on the underlying first order theory and therefore it does not involve any additional complexity caused by the nonmonotonicity of default logic. More precisely, for default theories consisting of
Autoepistemic Logics of Closed Beliefs and Logic Programming
 Proceedings of the First International Workshop on Logic Programming and Nonmonotonic Reasoning
, 1995
"... Moore's autoepistemic logic AEL proved to be a very successful approach to formalizing nonmonotonic reasoning and logic programming. However, AEL also has some important drawbacks, e.g., quite "reasonable" theories are often inconsistent in AEL, it does not always lead to the expec ..."
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Cited by 22 (10 self)
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Moore's autoepistemic logic AEL proved to be a very successful approach to formalizing nonmonotonic reasoning and logic programming. However, AEL also has some important drawbacks, e.g., quite "reasonable" theories are often inconsistent in AEL, it does not always lead to the expected, intended semantics and it cannot be effectively computed even for very simple classes of theories. In this paper we propose a more general approach to autoepistemic reasoning by introducing Autoepistemic Logics of Closed Beliefs AEL cl , where j= cl denotes a specific negative introspection inference operator ("closed world assumption") on which negative introspection in this logic is based. Negative introspection determines which formulae in autoepistemic logic are disbelieved, or, putting it differently, negation of which formulae can be assumed by default. It determines therefore the set of closed world beliefs derivable in a given autoepistemic logic. Moore's autoepistemic logic AEL is a specia...
Paraconsistent Declarative Semantics for Extended Logic Programs
 Annals of Mathematics and Artificial Intelligence
, 2002
"... We introduce a fixpoint semantics for logic programs with two kinds of negation:... ..."
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Cited by 20 (3 self)
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We introduce a fixpoint semantics for logic programs with two kinds of negation:...
Contradiction Removal Semantics with Explicit Negation
 KNOWLEDGE REPRESENTATION AND REASONING UNDER UNCERTAINTY, NUMBER 808 IN LNAI
, 1992
"... Well Founded Semantics for logic programs extended with eXplicit negation (WFSX) is characterized by that, in any model, whenever :a (the explicit negation of a) holds, then ¸a (the negation by default of a) also holds. When explicit negation is used contradiction may be present (e.g. a and :a bot ..."
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Cited by 16 (12 self)
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Well Founded Semantics for logic programs extended with eXplicit negation (WFSX) is characterized by that, in any model, whenever :a (the explicit negation of a) holds, then ¸a (the negation by default of a) also holds. When explicit negation is used contradiction may be present (e.g. a and :a both hold for some a) and thus no semantics is given to the program. We introduce here the notion of removing some contradictions, through identifying the set of models obtained by revising closed world assumptions. One such unique model is singled out as the contradiction free semantics (CRSX). When contradiction does not arise, the contradiction removal semantics coincides with WFSX.
An Encompassing Framework for Paraconsistent Logic Programs
 J. Applied Logic
, 2003
"... We propose a framework which extends Antitonic Logic Programs [13] to an arbitrary complete bilattice of truthvalues, where belief and doubt are explicitly represented. Inspired by Ginsberg and Fitting 's bilattice approaches, this framework allows a precise de nition of important operato ..."
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Cited by 16 (6 self)
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We propose a framework which extends Antitonic Logic Programs [13] to an arbitrary complete bilattice of truthvalues, where belief and doubt are explicitly represented. Inspired by Ginsberg and Fitting 's bilattice approaches, this framework allows a precise de nition of important operators found in logic programming, such as explicit and default negation. In particular, it leads to a natural semantical integration of explicit and default negation through the Coherence Principle [38], according to which explicit negation entails default negation. We then de ne Coherent Answer Sets, and the Paraconsistent Wellfounded Model semantics, generalising many paraconsistent semantics for logic programs. In particular, Paraconsistent WellFounded Semantics with eXplicit negation (WFSXp ) [3, 11]. The framework is an extension of Antitonic Logic Programs for most cases, and is general enough to capture Probabilistic Deductive Databases, Possibilistic Logic Programming, Hybrid Probabilistic Logic Programs, and Fuzzy Logic Programming. Thus, we have a powerful mathematical formalism for dealing simultaneously with default, paraconsistency, and uncertainty reasoning. Results are provided about how our semantical framework deals with inconsistent information and with its propagation by the rules of the program.
Adding Closed World Assumptions to Well Founded Semantics
 Theoretical Computer Science
, 1994
"... Given a program P we specify an enlargement of its Well Founded Model which gives meaning to the adding of Closed World Assumptions. We do so by proposing the desirable principles of a Closed World Assumption (CWA), and proceed to formally define and apply them to Well Founded Semantics (WFS), in or ..."
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Cited by 15 (6 self)
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Given a program P we specify an enlargement of its Well Founded Model which gives meaning to the adding of Closed World Assumptions. We do so by proposing the desirable principles of a Closed World Assumption (CWA), and proceed to formally define and apply them to Well Founded Semantics (WFS), in order to obtain a WFS added with CWA, the Osemantics. After an introduction and motivating examples, there follow the presentation of the concepts required to formalize the model structure, the properties it enjoys, and the criteria and procedures which allow the precise characterization of the preferred unique maximal model that gives the intended meaning to the OSemantics of a program, the OModel. Some properties are also exhibited that permit a more expedite obtention of the models. Several detailed examples are introduced throughout to illustrate the concepts and their application. Comparison is made with other work, and in the conclusions the novelty of the approach is brought out. 1 I...