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Using Ontologies to Query Probabilistic Numerical Data

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Frontiers of Combining Systems (FroCoS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10483))

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Abstract

We consider ontology-based query answering in a setting where some of the data are numerical and of a probabilistic nature, such as data obtained from uncertain sensor readings. The uncertainty for such numerical values can be more precisely represented by continuous probability distributions than by discrete probabilities for numerical facts concerning exact values. For this reason, we extend existing approaches using discrete probability distributions over facts by continuous probability distributions over numerical values. We determine the exact (data and combined) complexity of query answering in extensions of the well-known description logics \(\mathcal {EL}\) and \(\mathcal {ALC}\) with numerical comparison operators in this probabilistic setting.

Supported by the DFG within the collaborative research center SFB 912 (HAEC) and the research unit FOR 1513 (HYBRIS).

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Notes

  1. 1.

    Here, the set \(\mathbb {D} \subseteq \mathbb {R} \) denotes the dyadic rationals, that is, the set of all real numbers that have a finite number of bits after the binary point.

  2. 2.

    Note that the counting complexity classes considered here are all closed under this operation. To see this, consider f and g characterized by the relations R and \(R'\) s.t. \(R'=\{(x,y\#z) \mid R(x,y), z\in \{0,1\}^*,|z|=p(x)\}\). Clearly, \(g(x)=2^{p(x)}f(x)\).

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Authors and Affiliations

  1. Institute of Theoretical Computer Science, Technische Universität Dresden, Dresden, Germany

    Franz Baader, Patrick Koopmann & Anni-Yasmin Turhan

Authors
  1. Franz Baader
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  2. Patrick Koopmann
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  3. Anni-Yasmin Turhan
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Corresponding authors

Correspondence to Franz Baader , Patrick Koopmann or Anni-Yasmin Turhan .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Clare Dixon

  2. University of Sao Paulo, Sao Paulo, Brazil

    Marcelo Finger

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Baader, F., Koopmann, P., Turhan, AY. (2017). Using Ontologies to Query Probabilistic Numerical Data. In: Dixon, C., Finger, M. (eds) Frontiers of Combining Systems. FroCoS 2017. Lecture Notes in Computer Science(), vol 10483. Springer, Cham. https://doi.org/10.1007/978-3-319-66167-4_5

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  • DOI: https://doi.org/10.1007/978-3-319-66167-4_5

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