Reasoning with the finitely many-valued Łukasiewicz fuzzy Description Logic SROIQ☆

Bobillo, Fernando; Straccia, Umberto

doi:10.1016/j.ins.2010.10.020

Cited by 61 publications

(83 citation statements)

References 51 publications

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“…It is important to notice that under the product t-norm semantics, the models of an ontology may, in general, require infinitely many different interpretation values. Hence, the methods for transforming fuzzy DL ontologies into crisp DL ontologies [19], [20], [21] cannot be applied in this setting.…”

Section: Discussionmentioning

confidence: 99%

Are fuzzy description logics with general concept inclusion axioms decidable?

Baader

Peñaloza

2011

2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011)

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Abstract-This paper concentrates on a fuzzy Description Logic with product t-norm and involutive negation. It does not answer the question posed in its title for this logic, but it gives strong indications that the answer might in fact be "no." On the one hand, it shows that an algorithm that was claimed to answer the question affirmatively for this logic is actually incorrect. On the other hand, it proves undecidability of a variant of this logic.

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Section: Discussionmentioning

confidence: 99%

Are fuzzy description logics with general concept inclusion axioms decidable?

Baader

Peñaloza

2011

2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011)

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“…This differs from previous reductions for finitely valued FDLs [7,9,31] in that we not only consider cut-concepts of the form p C with p ∈ V O , but also relationships between different concepts. 8 We use the abbreviations α β := β α , α < β := ¬ α β , and similarly for = and >.…”

Section: The Reductionmentioning

confidence: 90%

Reasoning in Expressive Description Logics under Infinitely Valued Gödel Semantics

Borgwardt

Peñaloza

2015

Frontiers of Combining Systems

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Abstract. Fuzzy Description Logics (FDLs) combine classical Description Logics with the semantics of Fuzzy Logics in order to represent and reason with vague knowledge. Most FDLs using truth values from the interval [0, 1] have been shown to be undecidable in the presence of a negation constructor and general concept inclusions. One exception are those FDLs whose semantics is based on the infinitely valued Gödel tnorm (G). We extend previous decidability results for the FDL G-ALC to deal with complex role inclusions, nominals, inverse roles, and qualified number restrictions. Our novel approach is based on a combination of the known crispification technique for finitely valued FDLs and an automata-based procedure for reasoning in G-ALC.

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“…In this section, we provide a brief account to the fairly standard fuzzy DL f-SROIQ (see also [34,23,35]). This logic is of particular interest since it consists of the logical underpinnings of fuzzy OWL and fuzzy OWL 2 (excluding datatypes which we do not deal with here).…”

Section: Fuzzy Owl and Dlsmentioning

confidence: 99%

“…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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Reasoning with the finitely many-valued Łukasiewicz fuzzy Description Logic SROIQ☆

Cited by 61 publications

References 51 publications

Are fuzzy description logics with general concept inclusion axioms decidable?

Are fuzzy description logics with general concept inclusion axioms decidable?

Reasoning in Expressive Description Logics under Infinitely Valued Gödel Semantics

A Fuzzy Extension to the OWL 2 RL Ontology Language

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