Reasoning with qualified cardinality restrictions in fuzzy Description Logics

Stoilos, Giorgos; Stamou, Giorgos; Kollias, Stefanos

doi:10.1109/fuzzy.2008.4630436

Cited by 15 publications

(21 citation statements)

References 17 publications

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“…In addition, Sa´nchez and Tettamanzi (2006) defined independence of fuzzy assertions and obtained some results that speed up the calculation of fuzzy satisfiability in some (the most common) cases. More recently, Stoilos et al (2008a) investigated on the problem of reasoning with qualified cardinality restrictions in fuzzy DLs, extending previous results on simple number restrictions, and thus presented a tableaux algorithm for the fuzzy DL f-ALCIQ. The other efforts for extending fuzzy DLs with number restrictions (such as f KD -SHIN and fuzzy SHOIQ) can be found in Section 3.2.3.…”

Section: Fuzzy Description Logics With Number Restrictionsmentioning

confidence: 96%

An overview of fuzzy Description Logics for the Semantic Web

Zhang

Wang

et al. 2012

The Knowledge Engineering Review

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Information imprecision and uncertainty exist in many real world applications, and such information would be retrieved, processed, shared, reused, and aligned in the maximum automatic way possible. As a popular family of formally well-founded and decidable knowledge representation languages, fuzzy Description Logics (fuzzy DLs), which extend DLs with fuzzy logic, are very well suited to cover for representing and reasoning with imprecision and uncertainty. Thus, a requirement naturally arises in many practical applications of knowledge-based systems, in particular the Semantic Web, because DLs are the logical foundation of the Semantic Web. Currently, there have been lots of fuzzy extensions of DLs with Zadeh's fuzzy logic theory papers published, to investigate fuzzy DLs and more importantly serve as identifying the direction of fuzzy DLs study. In this paper, we aim at providing a comprehensive literature overview of fuzzy DLs, and we focus our attention on fuzzy extensions of DLs based on fuzzy set theory. Other relevant formalisms that are based on approaches like probabilistic theory or non-monotonic logics are covered elsewhere. In detail, we first introduce the existing fuzzy DLs (including the syntax, semantics, knowledge base, and reasoning algorithm) from the origin, development (from weaker to stronger in expressive power), some special techniques, and so on. Then, the other important issues on fuzzy DLs, such as reasoning, querying, applications, and directions for future research, are also discussed in detail. Also, we make a comparison and analysis.

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Section: Fuzzy Description Logics With Number Restrictionsmentioning

confidence: 96%

An overview of fuzzy Description Logics for the Semantic Web

Zhang

Wang

et al. 2012

The Knowledge Engineering Review

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“…The traditional Zadeh semantics takes up a special position in FDL research, as it underlies the only existing tableau algorithms that can deal with full GCIs and the expressivity of SHOIQ, without needing to solve mixed integer optimization problems [32,[49][50][51]. This is due to the fact that reasoning can be restricted to finitely many values, as described earlier.…”

Section: Related Workmentioning

confidence: 99%

Algorithms for reasoning in very expressive description logics under infinitely valued Gödel semantics

Borgwardt

Pealoza

2017

International Journal of Approximate Reasoning

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Fuzzy description logics (FDLs) are knowledge representation formalisms capable of dealing with imprecise knowledge by allowing intermediate membership degrees in the interpretation of concepts and roles. One option for dealing with these intermediate degrees is to use the so-called Gödel semantics, under which conjunction is interpreted by the minimum of the degrees of the conjuncts. Despite its apparent simplicity, developing reasoning techniques for expressive FDLs under this semantics is a hard task. In this paper, we introduce two new algorithms for reasoning in very expressive FDLs under Gödel semantics. They combine the ideas of a previous automata-based algorithm for Gödel FDLs with the known crispification and tableau approaches for FDL reasoning. The results are the two first practical algorithms capable of reasoning in infinitely valued FDLs supporting general concept inclusions.

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“…Since there are only finitely many possibilities for such assertions over a single individual, appropriate blocking conditions can ensure termination of these algorithms. Fuzzy tableaux algorithms have been developed, starting from the initial works in [95,96,106], for very expressive extensions of L-NALC with more concept constructors [38,43,88,89,92,93]. They usually do not provide tight complexity bounds for deciding consistency, but they have been successfully implemented in FDL reasoners like fuzzyDL [23] and FiRE [86].…”

Section: Zadeh and Finitely Valued Semanticsmentioning

confidence: 99%