Reasoning in Expressive Description Logics under Infinitely Valued Gödel Semantics

Borgwardt, Stefan; Peñaloza, Rafael

doi:10.1007/978-3-319-24246-0_4

Cited by 4 publications

(6 citation statements)

References 27 publications

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“…In this section, we extend the classical tableau construction from [23,30] with the ideas developed in [10,15] to produce a tableau-based reasoning algorithm capable of handling full G-SROIQ. Although this algorithm does not allow us to derive tight complexity bounds, it constructs a G-model in a goal-oriented way and exhibits the same pay-as-you-go behavior as the classical tableau algorithm [23].…”

Section: A Tableau Algorithmmentioning

confidence: 99%

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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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Section: A Tableau Algorithmmentioning

confidence: 99%

“…This algorithm has already been presented in the short conference paper[15] 2. For the scope of this paper, we limit the possible degrees to be rational numbers only.…”

mentioning

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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“…We show here that the negation can also be provided by the Łukasiewicz t-norm itself. Complementary decidability results again make use of reductions to classical DLs [8,48,49], or introduce automata-and tableau-based algorithms tailored towards the infinite Gödel t-norm [50,51].…”

Section: Related Workmentioning

confidence: 99%

The complexity of fuzzy EL under the Łukasiewicz T-norm

Borgwardt

Cerami

Peñaloza

2017

International Journal of Approximate Reasoning

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Fuzzy Description Logics (DLs) are are a family of knowledge representation formalisms designed to represent and reason about vague and imprecise knowledge that is inherent to many application domains. Previous work has shown that the complexity of reasoning in a fuzzy DL using finitely many truth degrees is usually not higher than that of the underlying classical DL. We show that this does not hold for fuzzy extensions of the lightweight DL EL, which is used in many biomedical ontologies, under the finitely valued Łukasiewicz semantics. More precisely, the complexity of reasoning increases from P to ExpTime, even if only one additional truth value is introduced. When adding complex role inclusions and inverse roles, the logic even becomes undecidable. Even more surprisingly, when considering the infinitely valued Łukasiewicz semantics, reasoning in fuzzy EL is undecidable.

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“…Moreover, only finitely many such orderings are relevant. Hence, a new crispification approach was developed in [44], where the classical concepts represent orderings between the degrees given to different fuzzy concepts. Building on this idea, a tableaux-based method, which decomposes complex concepts into simpler (ordered) concepts, was developed in [46].…”

Section: Gödel Semanticsmentioning

confidence: 99%

“…For example, more complex assertions like Tall(a) > Tall(b) allow to compare fuzzy degrees between different individuals a and b. Usually, such extensions do not affect the complexity of consistency [31,[44][45][46]. Going one step further, one can also allow comparisons inside concepts like Tall > ∀friend.Tall, representing the set of all people that are taller than all their friends.…”

Section: Related Notionsmentioning

confidence: 99%