How Fuzzy Is My Fuzzy Description Logic?

Borgwardt, Stefan; Distel, Felix; Peñaloza, Rafael

doi:10.1007/978-3-642-31365-3_9

Cited by 15 publications

(24 citation statements)

References 19 publications

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“…First we show that in the absence of zero divisors ontology consistency is linearly reducible to crisp consistency, regardless of the shape of the lattice, similarly to the result in [23]. For any…”

Section: Consistency Over Infinite Latticessupporting

confidence: 55%

“…For the class of continuous t-norms over the interval [0, 1], decidability has been almost fully characterized. In a nutshell, ontology consistency is decidable if (i) the t-norm is idempotent; that is, the Gödel t-norm [21,22], or (ii) the t-norm has no zero divisors and the involutive negation operator is disallowed [23]. With very few exceptions, all other cases are known to be undecidable [16,24].…”

Section: Snomed Ctmentioning

confidence: 99%

“…In fact, it has been shown that if the t-norm has no zero divisors, then consistency can be reduced in linear time to consistency of crisp ontologies [23]. On the other hand, for any t-norm having (infinitely many) zero divisors, 12 ontology consistency has been shown to be undecidable [16], even if we restrict expressivity to the logic L-NEL, allowing only existential restrictions, conjunctions, and residual negations, and all axioms hold with degree 1.…”

Section: Consistency Over Infinite Latticesmentioning

confidence: 99%

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Consistency reasoning in lattice-based fuzzy Description Logics

Borgwardt

Peñaloza

2014

International Journal of Approximate Reasoning

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Fuzzy Description Logics have been widely studied as a formalism for representing and reasoning with vague knowledge. One of the most basic reasoning tasks in (fuzzy) Description Logics is to decide whether an ontology representing a knowledge domain is consistent. Surprisingly, not much is known about the complexity of this problem for semantics based on complete De Morgan lattices. To cover this gap, in this paper we study the consistency problem for the fuzzy Description Logic L-SHI and its sublogics in detail.The contribution of the paper is twofold. On the one hand, we provide a tableaux-based algorithm for deciding consistency when the underlying lattice is finite. The algorithm generalizes the one developed for classical SHI. On the other hand, we identify decidable and undecidable classes of fuzzy Description Logics over infinite lattices. For all the decidable classes, we also provide tight complexity bounds.

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Section: Consistency Over Infinite Latticessupporting

confidence: 55%

Section: Snomed Ctmentioning

confidence: 99%

Section: Consistency Over Infinite Latticesmentioning

confidence: 99%

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Consistency reasoning in lattice-based fuzzy Description Logics

Borgwardt

Peñaloza

2014

International Journal of Approximate Reasoning

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“…Important examples are, extensions to tableaux algo-G. Stoilos et al rithms [11,17], implemented in the system FiRE [18], tableaux coupled with mixed integer linear programming algorithms [19,20], implemented in the system fuzzyDL [8], algorithms that reduce fuzzy DLs to crisp DLs [21,22,23], implemented in the DeLorean system [24], SMT-based methods [25], and the direct crispification method [26]. In addition, several optimisations have also been proposed [18,27].…”

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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“…However, on the one hand reasoning in fuzzy DLs easily becomes undecidable [6][7][8] and on the other hand depending on the user and on the request, different ways of relaxing the query concept are needed. For instance, for a request to a car rental company to rent a particular car model in Beijing, it might be acceptable to get an offer for a similar car model to be rented in Beijing, instead of getting the offer to rent the requested car model in London.…”

Section: Introductionmentioning

confidence: 99%

Similarity-based relaxed instance queries

Ecke

Peñaloza

Turhan

2015

Journal of Applied Logic

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In Description Logics (DL) knowledge bases (KBs), information is typically captured by clear-cut concepts. For many practical applications querying the KB by crisp concepts is too restrictive; a user might be willing to lose some precision in the query, in exchange of a larger selection of answers. Similarity measures can offer a controlled way of gradually relaxing a query concept within a user-specified limit.In this paper we formalize the task of instance query answering for DL KBs using concepts relaxed by concept similarity measures (CSMs). We investigate computation algorithms for this task in the DL EL, their complexity and properties for the CSMs employed regarding whether unfoldable or general TBoxes are used. For the case of general TBoxes we define a family of CSMs that take the full TBox information into account, when assessing the similarity of concepts.

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How Fuzzy Is My Fuzzy Description Logic?

Cited by 15 publications

References 19 publications

Consistency reasoning in lattice-based fuzzy Description Logics

Consistency reasoning in lattice-based fuzzy Description Logics

A Fuzzy Extension to the OWL 2 RL Ontology Language

Similarity-based relaxed instance queries

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