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Possibilistic stable models
 Nonmonotonic Reasoning, Answer Set Programming and Constraints, volume 05171 of Dagstuhl Seminar Proceedings. Internationales Begegnungs und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl
, 2005
"... In this work, we define a new framework in order to improve the knowledge representation power of Answer Set Programming paradigm. Our proposal is to use notions from possibility theory to extend the stable model semantics by taking into account a certainty level, expressed in terms of necessity mea ..."
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In this work, we define a new framework in order to improve the knowledge representation power of Answer Set Programming paradigm. Our proposal is to use notions from possibility theory to extend the stable model semantics by taking into account a certainty level, expressed in terms of necessity measure, on each rule of a normal logic program. First of all, we introduce possibilistic definite logic programs and show how to compute the conclusions of such programs both in syntactic and semantic ways. The syntactic handling is done by help of a fixpoint operator, the semantic part relies on a possibility distribution on all sets of atoms and we show that the two approaches are equivalent. In a second part, we define what is a possibilistic stable model for a normal logic program, with default negation. Again, we define a possibility distribution allowing to determine the stable models. 1
Annotated answer set programming
 In: Proceedings of the 11th International Conference on Information Processing and Management of Uncertainty in KnowledgeBased Systems (IPMU06
, 2006
"... We present Annotated Answer Set Programming, that extends the expressive power of disjunctive logic programming with annotation terms, taken from the generalized annotated logic programming framework. ..."
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We present Annotated Answer Set Programming, that extends the expressive power of disjunctive logic programming with annotation terms, taken from the generalized annotated logic programming framework.
A Completeness Theorem for MultiAdjoint Logic Programming
 In Proc. FUZZIEEE’01. The 10th IEEE International Conference on Fuzzy Systems, IEEE
, 2001
"... Mukiadjoint logic programs generalise monotonic and residuated logic pro grams [21 in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. As our approach has continuous fixpoint semantics, in this work, a procedural semantics is g ..."
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Cited by 6 (2 self)
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Mukiadjoint logic programs generalise monotonic and residuated logic pro grams [21 in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. As our approach has continuous fixpoint semantics, in this work, a procedural semantics is given for the paradigm of multiadjoint logic programming and a completeness result is proved.
On Termination of a Tabulation Procedure for Residuated Logic Programming
 6th Intl Workshop on Termination
, 2003
"... Residuated Logic Programs allow to capture a spate of different semantics dealing with uncertainty and vagueness. A first result states that for any definite residuated logic program the sequence of iterations of the immediate consequences operator reaches the least fixpoint after only finitely m ..."
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Cited by 5 (4 self)
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Residuated Logic Programs allow to capture a spate of different semantics dealing with uncertainty and vagueness. A first result states that for any definite residuated logic program the sequence of iterations of the immediate consequences operator reaches the least fixpoint after only finitely many steps. Then, a tabulation query procedure is introduced, and it is shown that the procedure terminates every definite residuated logic program.
A MultiAdjoint Logic Approach to Abductive Reasoning
 In Logic Programming, ICLP’01
, 2001
"... Multiadjoint logic programs has been recently introduced [9, 10] as a generalization of monotonic logic programs [2, 3], in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. ..."
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Cited by 4 (4 self)
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Multiadjoint logic programs has been recently introduced [9, 10] as a generalization of monotonic logic programs [2, 3], in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed.
Towards Biresiduated MultiAdjoint Logic Programming
 IN PROC. CAEPIA’03, LECT. NOTES IN ARTIFICIAL INTELLIGENCE 3040:608–617
, 2003
"... Multiadjoint logic programs were recently proposed as a generalization of monotonic and residuated logic programs, in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. In this work, the need of biresiduated pairs is justified thr ..."
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Cited by 4 (3 self)
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Multiadjoint logic programs were recently proposed as a generalization of monotonic and residuated logic programs, in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. In this work, the need of biresiduated pairs is justified through the study of a very intuitive family of operators, which turn out to be not necessarily commutative and associative and, thus, might have two different residuated implications; finally, we introduce the framework of biresiduated multiadjoint logic programming and sketch some considerations on its fixpoint semantics.
Arguments and Misunderstandings: Fuzzy Unification for Negotiating Agents
 Electronic Notes in Theoretical Computer Science
"... In this paper, we develop the notion of fuzzy unification and incorporate it into a novel fuzzy argumentation framework for extended logic programming. We make the following contributions: The argumentation framework is defined by a declarative bottomup fixpoint semantics and an equivalent goal ..."
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In this paper, we develop the notion of fuzzy unification and incorporate it into a novel fuzzy argumentation framework for extended logic programming. We make the following contributions: The argumentation framework is defined by a declarative bottomup fixpoint semantics and an equivalent goaldirected topdown proofprocedure for extended logic programming. Our framework allows one to represent positive and explicitly negative knowledge, as well as uncertainty. Both concepts are used in agent communication languages such as KQML and FIPA ACL. One source of uncertainty in open systems stems from mismatches in parameter and predicate names and missing parameters. To this end, we conservatively extend classical unification and develop fuzzy unification based on normalised edit distance over trees.
Tabling with answer subsumption: Implementation, applications and performance
 In JELIA. 300–312
, 2010
"... Abstract. Tabled Logic Programming (TLP) is becoming widely available in Prolog systems, but most implementations of TLP implement only answer variance in which an answer A is added to the table for a subgoal S only if A is not a variant of any other answer already in the table for S. While TLP with ..."
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Abstract. Tabled Logic Programming (TLP) is becoming widely available in Prolog systems, but most implementations of TLP implement only answer variance in which an answer A is added to the table for a subgoal S only if A is not a variant of any other answer already in the table for S. While TLP with answer variance is powerful enough to implement the wellfounded semantics with good termination and complexity properties, TLP becomes much more powerful if a mechanism called answer subsumption is used. XSB implements two forms of answer subsumption. The first, partial order answer subsumption, adds A to a table only if A is greater than all other answers already in the table according to a userdefined partial order. The second, lattice answer subsumption, may join A to some other answer in the table according to a userdefined upper semilattice. Answer subsumption can be used to implement paraconsistent and quantitative logics, abstract analysis domains, and preference logics. This paper discusses the semantics and implementation of answer subsumption in XSB, and discusses performance and scalability of answer subsumption on a variety of problems. 1
Multilattices as a basis for generalized fuzzy logic programming
 WILF 2005. LNCS (LNAI
, 2006
"... Abstract. A prospective study of the use of ordered multilattices as underlying sets of truthvalues for a generalised framework of logic programming is presented. Specifically, we investigate the possibility of using multilatticevalued interpretations of logic programs and the theoretical proble ..."
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Abstract. A prospective study of the use of ordered multilattices as underlying sets of truthvalues for a generalised framework of logic programming is presented. Specifically, we investigate the possibility of using multilatticevalued interpretations of logic programs and the theoretical problems that this generates with regard to its fixed point semantics. 1
A neural implementation of multiadjoint logic programming
 Journal of Applied Logic
, 2004
"... A generalization of the homogenization process needed for the neural implementation of multiadjoint logic programming (a unifying theory to deal with uncertainty, imprecise data or incomplete information) is presented here. The idea is to allow to represent a more general family of adjoint pairs, b ..."
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A generalization of the homogenization process needed for the neural implementation of multiadjoint logic programming (a unifying theory to deal with uncertainty, imprecise data or incomplete information) is presented here. The idea is to allow to represent a more general family of adjoint pairs, but maintaining the advantage of the existing implementation recently introduced in [6]. The soundness of the transformation is proved and its complexity is analysed. In addition, the corresponding generalization of the neurallike implementation of the fixed point semantics of multiadjoint is presented. 1