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Counting and Conjunctive Queries in the Lifted Junction Tree Algorithm

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Book cover Graph Structures for Knowledge Representation and Reasoning (GKR 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10775))

Abstract

Standard approaches for inference in probabilistic formalisms with first-order constructs include lifted variable elimination (LVE) for single queries. To handle multiple queries efficiently, the lifted junction tree algorithm (LJT) uses a first-order cluster representation of a knowledge base and LVE in its computations. We extend LJT with a full formal specification of its algorithm steps incorporating (i) the lifting tool of counting and (ii) answering of conjunctive queries. Given multiple queries, e.g., in machine learning applications, our approach enables us to compute answers faster than the current LJT and existing approaches tailored for single queries.

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Authors and Affiliations

  1. Institute of Information Systems, Universität zu Lübeck, Lübeck, Germany

    Tanya Braun & Ralf Möller

Authors
  1. Tanya Braun
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  2. Ralf Möller
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Correspondence to Tanya Braun .

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Editors and Affiliations

  1. LIRMM, Montpellier Cedex 5, France

    Madalina Croitoru

  2. CRIL-CNRS and Université d’Artois, Lens, France

    Pierre Marquis

  3. Technische Universität Dresden, Dresden, Germany

    Sebastian Rudolph

  4. University of Brighton, Brighton, United Kingdom

    Gem Stapleton

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Braun, T., Möller, R. (2018). Counting and Conjunctive Queries in the Lifted Junction Tree Algorithm. In: Croitoru, M., Marquis, P., Rudolph, S., Stapleton, G. (eds) Graph Structures for Knowledge Representation and Reasoning. GKR 2017. Lecture Notes in Computer Science(), vol 10775. Springer, Cham. https://doi.org/10.1007/978-3-319-78102-0_3

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  • DOI: https://doi.org/10.1007/978-3-319-78102-0_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78101-3

  • Online ISBN: 978-3-319-78102-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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