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32
Similaritybased unification: a multiadjoint approach. Fuzzy sets and systems
 In Proc. EUSFLAT Conference in Fuzzy Logic and Technology
, 2002
"... The aim of this paper is to build a formal model for fuzzy unification in multiadjoint logic programs containing both a declarative and a procedural part, and prove its soundness and completeness. Our approach is based on a general framework for logic programming, which gives a formal model of fuzz ..."
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Cited by 52 (15 self)
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The aim of this paper is to build a formal model for fuzzy unification in multiadjoint logic programs containing both a declarative and a procedural part, and prove its soundness and completeness. Our approach is based on a general framework for logic programming, which gives a formal model of fuzzy logic programming extended by fuzzy similarities and axioms of firstorder logic with equality.
Managing uncertainty and vagueness in description logics, logic Reducing Fuzzy Answer Set Programming to Model Finding in Fuzzy Logics 33 programs and description logic programs
 In Reasoning Web: 4th International Summer School 2008
"... Abstract. Managing uncertainty and/or vagueness is starting to play an important role in Semantic Web representation languages. Our aim is to overview basic concepts on representing uncertain and vague knowledge in current Semantic Web ontology and rule languages (and their combination). 1 ..."
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Cited by 23 (5 self)
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Abstract. Managing uncertainty and/or vagueness is starting to play an important role in Semantic Web representation languages. Our aim is to overview basic concepts on representing uncertain and vague knowledge in current Semantic Web ontology and rule languages (and their combination). 1
Termination Results for Sorted MultiAdjoint Logic Programs
 In Information Processing and Management of Uncertainty for KnowledgeBased Systems, IPMU’04. Accepted
"... In this paper we present a logic programmingbased language allowing for the combination of several adjoint lattices of truthvalues. A model and xpoint theory are presented, but the main contribution of the paper is the study of general properties guaranteeing termination of all queries. New ..."
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Cited by 11 (4 self)
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In this paper we present a logic programmingbased language allowing for the combination of several adjoint lattices of truthvalues. A model and xpoint theory are presented, but the main contribution of the paper is the study of general properties guaranteeing termination of all queries. New results are presented and related to other alternative formalisms.
A Neural Approach to Abductive MultiAdjoint Reasoning
 In AI  Methodologies, Systems, Applications. AIMSA’02
, 2002
"... A neural approach to propositional multiadjoint logic programming was recently introduced. In this paper we extend the neural approach to multiadjoint deduction and, furthermore, modify it to cope with abductive multiadjoint reasoning, where adaptations of the uncertainty factor in a knowledg ..."
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Cited by 9 (5 self)
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A neural approach to propositional multiadjoint logic programming was recently introduced. In this paper we extend the neural approach to multiadjoint deduction and, furthermore, modify it to cope with abductive multiadjoint reasoning, where adaptations of the uncertainty factor in a knowledge base are carried out automatically so that anumber of given observations can be adequately explained.
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.
Similaritybased Reasoning in Qualified Logic Programming Revised Edition
"... Similaritybased Logic Programming (briefly, SLP) has been proposed to enhance the LP paradigm with a kind of approximate reasoning which supports flexible information retrieval applications. This approach uses a fuzzy similarity relation R between symbols in the program’s signature, while keepin ..."
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Cited by 6 (3 self)
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Similaritybased Logic Programming (briefly, SLP) has been proposed to enhance the LP paradigm with a kind of approximate reasoning which supports flexible information retrieval applications. This approach uses a fuzzy similarity relation R between symbols in the program’s signature, while keeping the syntax for program clauses as in classical LP. Another recent proposal is the QLP (D) scheme for Qualified Logic Programming, an extension of the LP paradigm which supports approximate reasoning and more. This approach uses annotated program clauses and a parametrically given domain D whose elements qualify logical assertions by measuring their closeness to various users ’ expectations. In this paper we propose a more expressive scheme SQLP (R,D) which subsumes both SLP and QLP (D) as particular cases. We also show that SQLP (R,D) programs can be transformed into semantically equivalent QLP (D) programs. As a consequence, existing QLP (D) implementations can be used to give efficient support for similaritybased reasoning.
Operational/Interpretive Unfolding of Multiadjoint Logic Programs
"... Abstract: Multiadjoint logic programming represents a very recent, extremely flexible attempt for introducing fuzzy logic into logic programming. In this setting, the execution of a goal w.r.t. a given program is done in two separate phases. During the operational one, admissible steps are systemat ..."
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Cited by 6 (5 self)
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Abstract: Multiadjoint logic programming represents a very recent, extremely flexible attempt for introducing fuzzy logic into logic programming. In this setting, the execution of a goal w.r.t. a given program is done in two separate phases. During the operational one, admissible steps are systematically applied in a similar way to classical resolution steps in pure logic programming, thus returning a computed substitution together with an expression where all atoms have been exploited. This last expression is then interpreted under a given lattice during the so called interpretive phase, hence returning a value which represents the fuzzy component (truth degree) of the computed answer. On the other hand, unfolding is a well known transformation rule widely used in declarative programming for optimizing and specializing programs, among other applications. In essence, it is usually based on the application of operational steps on the body of program rules. The novelty of this paper consists in showing that this process can also be made in terms of interpretive steps. We present two strongly related kinds of unfolding (operational and interpretive), which, apart from exhibiting strong correctness properties (i.e. they preserve the semantics of computed substitutions and truth degrees) they are able to significantly simplify the two execution phases when solving goals.
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. This paper ..."
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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. This paper
2010b. Fixpoint & Prooftheoretic Semantics for CLP with Qualification and Proximity
"... Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause annotations based on uncertain truth values, qualification values a ..."
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Cited by 3 (0 self)
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Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause annotations based on uncertain truth values, qualification values as a generalization of uncertain truth values, and unification based on proximity relations. On the other hand, the CLP scheme has established itself as a powerful extension of LP that supports efficient computation over specialized domains while keeping a clean declarative semantics. In this report we propose a new scheme SQCLP designed as an extension of CLP that supports qualification values and proximity relations. We show that several previous proposals can be viewed as particular cases of the new scheme, obtained by partial instantiation. We present a declarative semantics for SQCLP that is based on observables, providing fixpoint and prooftheoretical characterizations of least program models as well as an implementationindependent notion of goal solutions.