Tractable reasoning with vague knowledge using fuzzy $\mathcal{EL}^{++}$

Mailis, Theofilos; Stoilos, Giorgos; Simou, Nikolaos; Stamou, Giorgos; Kollias, Stefanos

doi:10.1007/s10844-012-0195-6

Cited by 11 publications

(22 citation statements)

References 16 publications

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“…On the positive side, p-subsumption in G-EL can be decided in polynomial time in the size of the input ontology [5]. However, p-subsumption is co-NP-hard in ⊗-EL whenever ⊗ contains the Łukasiewicz t-norm [42].…”

Section: Subsumption and Instance Checkingmentioning

confidence: 99%

“…Moreover, we first proved in [23] that in ⊗-SHOI f,≥ for any t-norm ⊗ without zero divisors, the values in the input ontology do not have any effect in the consistency of the ontology, and can simply be removed (see Section 4). The inexpressive DL EL also keeps its polynomial complexity for subsumption under Gödel semantics [5].…”

Section: Related Workmentioning

confidence: 99%

“…For the last two decades, research on fuzzy DLs has covered many different logics, from the inexpressive EL [5] to the expressive SROIQ(D) [6], from simple fuzzy semantics [7] to ones covering all continuous t-norms [8], from acyclic terminologies [9] to GCIs [10]. Fuzzy reasoning algorithms were implemented [11,12] and the use of fuzziness in practical applications was studied [13,14].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The limits of decidability in fuzzy description logics with general concept inclusions

Borgwardt

Distel

Peñaloza

2015

Artificial Intelligence

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Fuzzy Description Logics (DLs) can be used to represent and reason with vague knowledge. This family of logical formalisms is very diverse, each member being characterized by a specific choice of constructors, axioms, and triangular norms, which are used to specify the semantics. Unfortunately, it has recently been shown that the consistency problem in many fuzzy DLs with general concept inclusion axioms is undecidable. In this paper, we present a proof framework that allows us to extend these results to cover large classes of fuzzy DLs. On the other hand, we also provide matching decidability results for most of the remaining logics. As a result, we obtain a near-universal classification of fuzzy DLs according to the decidability of their consistency problem.

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Section: Subsumption and Instance Checkingmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The limits of decidability in fuzzy description logics with general concept inclusions

Borgwardt

Distel

Peñaloza

2015

Artificial Intelligence

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“…Secondly, we feel that the issue of unsupported axioms is of further theoretical interest. It was recently shown that reasoning with fuzzy-EL 8 when conjunction is interpreted under several wellknown non-idempotent t-norms is co-NP-hard [58], despite the fact that the same language under the min t-norm has been shown to be polynominal [59]. Hence, the fact that such axioms fall outside fuzzy OWL 2 RL under such operators is perhaps an indicator that reasoning with them is hard (recall that OWL 2 RL is specifically designed to be polynomial).…”

Section: Discussionmentioning

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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“…This allows for a more fine-grained modelling for vague information as, for instance, in situation recognition in context-aware systems or even to model fuzzy spatial relations for image recognition. The combination of DLs and fuzzy concrete domains has been investigated already in a number of settings [11,3,9,8]. However, fuzzy DLs can easily turn out to be undecidable [4].…”

Section: Introductionmentioning

confidence: 99%

Reasoning in ${\mathcal{ALC}}$ with Fuzzy Concrete Domains

Merz

Peñaloza

Turhan

2014

Lecture Notes in Computer Science

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In the context of Description Logics (DLs) concrete domains allow to model concepts and facts by the use of concrete values and predicates between them. For reasoning in the DL ALC with general TBoxes concrete domains may cause undecidability. Under certain restrictions of the concrete domains decidability can be regained. Typically, the concrete domain predicates are crisp, which is a limitation for some applications. In this paper we investigate crisp ALC in combination with fuzzy concrete domains for general TBoxes, devise conditions for decidability, and give a tableau-based reasoning algorithm.

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Tractable reasoning with vague knowledge using fuzzy $\mathcal{EL}^{++}$

Cited by 11 publications

References 16 publications

The limits of decidability in fuzzy description logics with general concept inclusions

The limits of decidability in fuzzy description logics with general concept inclusions

A Fuzzy Extension to the OWL 2 RL Ontology Language

Reasoning in ${\mathcal{ALC}}$ with Fuzzy Concrete Domains

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