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Formal concept analysis via multiadjoint concept lattices
 Fuzzy Sets and Systems
"... Several fuzzifications of formal concept analysis have been proposed to deal with uncertain information. In this paper, we focus on concept lattices under a multiadjoint paradigm, which enriches the language providing greater flexibility to the user in that she can choose from a number of different ..."
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Cited by 31 (16 self)
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Several fuzzifications of formal concept analysis have been proposed to deal with uncertain information. In this paper, we focus on concept lattices under a multiadjoint paradigm, which enriches the language providing greater flexibility to the user in that she can choose from a number of different connectives. Multiadjoint concept lattices are shown to embed different fuzzy extensions of concept lattices found in the literature, the main results of the paper being the representation theorem of this paradigm and the embedding of other wellknown approaches.
Managing uncertainty and vagueness in description logics, logic programs and description logic programs
, 2008
"... 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). ..."
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Cited by 22 (6 self)
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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).
Multiadjoint tconcept lattices
, 2009
"... The tconcept lattice is introduced as a set of triples associated to graded tabular information interpreted in a noncommutative fuzzy logic. Following the general techniques of formal concept analysis, and based on the works by Georgescu and Popescu, given a noncommutative conjunctor it is possib ..."
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Cited by 19 (10 self)
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The tconcept lattice is introduced as a set of triples associated to graded tabular information interpreted in a noncommutative fuzzy logic. Following the general techniques of formal concept analysis, and based on the works by Georgescu and Popescu, given a noncommutative conjunctor it is possible to provide generalizations of the mappings for the intension and the extension in two different ways, and this generates a pair of concept lattices. In this paper, we show that the information common to both concept lattices can be seen as a sublattice of the Cartesian product of both concept lattices. The multiadjoint framework can be applied to this general tconcept lattice, and its usefulness is illustrated by a working example.
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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Cited by 15 (0 self)
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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.
On coherence and consistence in fuzzy answer set semantics for residuated logic programs
 Lect. Notes in Computer Science
"... Abstract. In this work we recall the first steps towards the definition of an answer set semantics for residuated logic programs with negation, and concentrate on the development of relationships between the notions of coherence and consistence of an interpretation. 1 ..."
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Cited by 12 (4 self)
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Abstract. In this work we recall the first steps towards the definition of an answer set semantics for residuated logic programs with negation, and concentrate on the development of relationships between the notions of coherence and consistence of an interpretation. 1
M.: Towards a fuzzy answer set semantics for residuated logic programs
 In: Web Intelligence/IAT Workshops, IEEE
, 2008
"... In this work we introduce the first steps towards the definition of an answer set semantics for residuated logic programs with negation. 1. ..."
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Cited by 11 (3 self)
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In this work we introduce the first steps towards the definition of an answer set semantics for residuated logic programs with negation. 1.
On multiadjoint concept lattices: definition and representation theorem
 Lect. Notes in Computer Science
, 2007
"... Abstract. Several fuzzifications of formal concept analysis have been proposed to deal with uncertainty or incomplete information. In this paper, we focus on the new paradigm of multiadjoint concept lattices which embeds different fuzzy extensions of concept lattices, our main result being the repr ..."
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Cited by 8 (5 self)
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Abstract. Several fuzzifications of formal concept analysis have been proposed to deal with uncertainty or incomplete information. In this paper, we focus on the new paradigm of multiadjoint concept lattices which embeds different fuzzy extensions of concept lattices, our main result being the representation theorem of this paradigm. As a consequence of this theorem, the representation theorems of the other paradigms can be proved more directly. Moreover, the multiadjoint paradigm enriches the language providing greater flexibility to the user.
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.
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.
Multiadjoint concept lattices
"... Abstract. Multiadjoint concept lattices were introduced [2,3] as a new general approach to formal concept analysis, in which the philosophy of the multiadjoint paradigm [1,4] to formal concept analysis is applied. With the idea of providing a general framework in which different approaches could b ..."
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Abstract. Multiadjoint concept lattices were introduced [2,3] as a new general approach to formal concept analysis, in which the philosophy of the multiadjoint paradigm [1,4] to formal concept analysis is applied. With the idea of providing a general framework in which different approaches could be conveniently accommodated, the authors worked in a general noncommutative environment; and this naturally lead to the consideration of adjoint triples, also called implication triples or biresiduated structure as the main building blocks of a multiadjoint concept lattice. In recent years there has been an increased interest in studying formal concept analysis on the perspective of using noncommutative conjunctors. This is not a mere mathematicalgeneralization,butarealneedsince,forinstance,whenonelearnsaconjunction from examples it is not unusual that the resulting conjunction does not satisfy commutativity. Different authors have argued in favour of considering noncommutative conjunctors. Actually, there exist quite reasonable examples of noncommutative and even nonassociative conjunctors defined on a regular partition of the unit interval. Hence, the possibility of considering noncommutative conjunctors provides more flexibility and increases the number of applications. This is one of the properties that the multiadjoint concept lattice framework offers. Another important feature is that different preferences among the set of attributes or/and objects can be considered. Moreover, this framework has been extended following different lines and has been applied to define general extensions of fuzzy rough sets theory, to solve fuzzy relation equations, etc.