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International Conference on Language and Automata Theory and Applications

LATA 2017: Language and Automata Theory and Applications pp 3–26Cite as

Approximation in Description Logics: How Weighted Tree Automata Can Help to Define the Required Concept Comparison Measures in \(\mathcal {FL}_0\)

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10168))

Abstract

Recently introduced approaches for relaxed query answering, approximately defining concepts, and approximately solving unification problems in Description Logics have in common that they are based on the use of concept comparison measures together with a threshold construction. In this paper, we will briefly review these approaches, and then show how weighted automata working on infinite trees can be used to construct computable concept comparison measures for \(\mathcal {FL}_0\) that are equivalence invariant w.r.t. general TBoxes. This is a first step towards employing such measures in the mentioned approximation approaches.

P. Marantidis—Supported by DFG Graduiertenkolleg 1763 (QuantLA).

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Notes

  1. 1.

    Note that this function is well-defined only for finite languages. Thus, \(e_2\) cannot be used in the presence of general TBoxes, where the languages may be infinite.

  2. 2.

    In the literature, more general forms of discounting have been introduced, where the tuple of endomorphisms to be used depends also on the label of a node, but here we restrict our attention to the simpler form of discounting introduced above.

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Authors and Affiliations

  1. Theoretical Computer Science, TU Dresden, Dresden, Germany

    Franz Baader, Oliver Fernández Gil & Pavlos Marantidis

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  1. Franz Baader
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  2. Oliver Fernández Gil
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  3. Pavlos Marantidis
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Correspondence to Franz Baader .

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Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Frank Drewes

  2. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  3. University of Giessen, Giessen, Germany

    Bianca Truthe

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Baader, F., Fernández Gil, O., Marantidis, P. (2017). Approximation in Description Logics: How Weighted Tree Automata Can Help to Define the Required Concept Comparison Measures in \(\mathcal {FL}_0\) . In: Drewes, F., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2017. Lecture Notes in Computer Science(), vol 10168. Springer, Cham. https://doi.org/10.1007/978-3-319-53733-7_1

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  • DOI: https://doi.org/10.1007/978-3-319-53733-7_1

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