Fuzzy description logics under Gödel semantics

Bobillo, Fernando; Delgado, Miguel; Gómez‐Romero, Juan; Straccia, Umberto

doi:10.1016/j.ijar.2008.10.003

Cited by 96 publications

(130 citation statements)

References 35 publications

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“…The majority of the reasoning algorithms available have been developed for the Gödel semantics, either by a reduction to crisp reasoning [6], or by a simple adaptation of the known algorithms for crisp DLs [23,24,25,27]. However, methods capable of dealing with other t-norms have also been explored [7,8,9,26,22].…”

Section: Introductionmentioning

confidence: 99%

How Fuzzy Is My Fuzzy Description Logic?

Borgwardt

Distel

Peñaloza

2012

Automated Reasoning

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Abstract. Fuzzy Description Logics (DLs) with t-norm semantics have been studied as a means for representing and reasoning with vague knowledge. Recent work has shown that even fairly inexpressive fuzzy DLs become undecidable for a wide variety of t-norms. We complement those results by providing a class of t-norms and an expressive fuzzy DL for which ontology consistency is linearly reducible to crisp reasoning, and thus has its same complexity. Surprisingly, in these same logics crisp models are insufficient for deciding fuzzy subsumption.

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Section: Introductionmentioning

confidence: 99%

How Fuzzy Is My Fuzzy Description Logic?

Borgwardt

Distel

Peñaloza

2012

Automated Reasoning

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“…Fuzzy Description Logics (FDLs) are natural extensions of DLs expressing vague concepts commonly present in real applications (see for instance [9,45,56,57,59,60]). Hájek [36] proposed to deal with FDLs taking as basis t-norm based fuzzy logics.…”

Section: Introductionmentioning

confidence: 99%

On similarity in fuzzy description logics

Armengol

Dellunde

García-Cerdaña

2016

Fuzzy Sets and Systems

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This paper is a contribution to the study of similarity relations between objects represented as attribute-value pairs in Fuzzy Description Logics. For this purpose we use concrete domains in the fuzzy description logic IALCE F (D) associated either with a left-continuous or with a finite t-norm. We propose to expand this fuzzy description logic by adding a Similarity Box (SBox) including axioms expressing properties of fuzzy equalities. We also define a global similarity between objects from similarities between the values of each object attribute (local similarities) and we prove that the global similarity defined using a t-norm inherits the usual properties of the local similarities (reflexivity, symmetry or transitivity). We also prove a result relative to global similarities expressing that, in the context of the logic MTL∀, similar objects have similar properties, being these properties expressed by predicate formulas evaluated in these objects.

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“…Managing fuzzy knowledge is of great importance in many applications, like multimedia processing [5,6], decision making [7], negotiation [8], and more. For these reasons many fuzzy extensions to OWL and DLs have been proposed [9,10,11,12,13,14,15,16,17]. Using fuzzy DLs we can state axioms like GoodDoctor(a) = 0.8 and GoodDoctor(b) = 0.7 which capture the fact that "a" is a better doctor than "b".…”

Section: Introductionmentioning

confidence: 99%

A Fuzzy Extension to the OWL 2 RL Ontology Language

Stoilos

Venetis

Stamou

2015

The Computer Journal

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Fuzzy extensions to Description Logics (DLs) have gained considerable attention the last decade. So far most works on fuzzy DLs have focused on either very expressive languages, like fuzzy OWL and OWL 2, or on highly inexpressive ones, like fuzzy OWL 2 QL and fuzzy OWL 2 EL. To the best of our knowledge a fuzzy extension to the language OWL 2 RL has not been thoroughly studied so far. This language is very relevant since it combines both adequate expressive power as well as efficient reasoning algorithms which can be realised using rule-based (Datalog) technologies. In contrast to previous fuzzy extensions, a fuzzy extension of OWL 2 RL is not a straightforward task for the following reason. The main motivation of OWL 2 RL is that its axioms can be equivalently represented as Datalog rules. Hence, to achieve our goal we need to investigate which OWL 2 RL axioms when interpreted under the fuzzy setting can be transformed to equivalent fuzzy Datalog rules. We show that this is not, in general, possible for all axioms but we show that this "issue" can to a large extent be alleviated. Moreover, we have performed an experimental evaluation with many well-known ontologies which showed that such axioms are not used so often in practice.

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Fuzzy description logics under Gödel semantics

Cited by 96 publications

References 35 publications

How Fuzzy Is My Fuzzy Description Logic?

How Fuzzy Is My Fuzzy Description Logic?

On similarity in fuzzy description logics

A Fuzzy Extension to the OWL 2 RL Ontology Language

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