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Extending Bell Numbers for Parsimonious Chase Estimation

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Logics in Artificial Intelligence (JELIA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11468))

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Abstract

Ontology-Based Query Answering (OBQA) consists in querying databases by taking ontological knowledge into account. We focus on a logical framework based on existential rules or tuple generating dependencies (TGDs), also known as Datalog\(^\pm \), which collects the basic decidable classes of TGDs, and generalizes several ontology specification languages, such as Description Logics. A fundamental notion to find certain answers to a query is the chase. This tool has been widely used to deal with different problems in databases, as it has the fundamental property of constructing a universal model. Recently, the so-called “parsimonious” chase procedure has been introduced. For some classes, it is sound and complete, and the termination is always guaranteed. However, no precise bound has been provided so far. To this end, we exploit the Bell number definition to count the exact maximal number of atoms generating by the parsimonious chase procedure.

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Acknowledgments

This work has been partially supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement No. 690974 for the project “MIREL: MIning and REasoning with Legal texts”.

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Authors and Affiliations

  1. University of Calabria, Rende, Italy

    Giovanni Amendola & Cinzia Marte

Authors
  1. Giovanni Amendola
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  2. Cinzia Marte
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Correspondence to Cinzia Marte .

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Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Francesco Calimeri

  2. University of Calabria, Rende, Italy

    Nicola Leone

  3. Mathematics and Computer Science, University of Calabria, Rende, Italy

    Marco Manna

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Amendola, G., Marte, C. (2019). Extending Bell Numbers for Parsimonious Chase Estimation. In: Calimeri, F., Leone, N., Manna, M. (eds) Logics in Artificial Intelligence. JELIA 2019. Lecture Notes in Computer Science(), vol 11468. Springer, Cham. https://doi.org/10.1007/978-3-030-19570-0_32

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  • DOI: https://doi.org/10.1007/978-3-030-19570-0_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-19569-4

  • Online ISBN: 978-3-030-19570-0

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