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European Conference on Logics in Artificial Intelligence

JELIA 2021: Logics in Artificial Intelligence pp 179–193Cite as

Exploiting Forwardness: Satisfiability and Query-Entailment in Forward Guarded Fragment

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 12678)

Abstract

We study the complexity of two standard reasoning problems for Forward Guarded Logic (\(\mathcal {FGF}\)), obtained as a restriction of the Guarded Fragment in which variables appear in atoms only in the order of their quantification. We show that \(\mathcal {FGF}\) enjoys the higher-arity-forest-model property, which results in \(\textsc {ExpTime}\)-completeness of its (finite and unrestricted) knowledge-base satisfiability problem. Moreover, we show that \(\mathcal {FGF}\) is well-suited for knowledge representation. By employing a generalisation of Lutz’s spoiler technique, we prove that the conjunctive query entailment problem for \(\mathcal {FGF}\) remains in \(\textsc {ExpTime}\).

We find that our results are quite unusual as \(\mathcal {FGF}\) is, up to our knowledge, the first decidable fragment of First-Order Logic, extending standard description logics like \(\mathcal {ALC}\), that offers unboundedly many variables and higher-arity relations while keeping its complexity surprisingly low.

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Acknowledgements

The author apologises for all mistakes and grammar issues that appear in the paper. He thanks A. Karykowska and P. Witkowski for proofreading, E. Kieroński for his help with the introduction, W. Faber for deadline extension and anonymous JELIA’s reviewers for many useful comments.

This work was supported by the ERC Consolidator Grant No. 771779 (DeciGUT).

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Authors and Affiliations

  1. Computational Logic Group, Technische Universität Dresden, Dresden, Germany

    Bartosz Bednarczyk

  2. Institute of Computer Science, University of Wrocław, Wrocław, Poland

    Bartosz Bednarczyk

Authors
  1. Bartosz Bednarczyk
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Correspondence to Bartosz Bednarczyk .

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Editors and Affiliations

  1. University of Klagenfurt, Klagenfurt, Austria

    Wolfgang Faber

  2. University of Klagenfurt, Klagenfurt, Austria

    Gerhard Friedrich

  3. University of Klagenfurt, Klagenfurt, Austria

    Martin Gebser

  4. University of Klagenfurt, Klagenfurt, Austria

    Michael Morak

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Bednarczyk, B. (2021). Exploiting Forwardness: Satisfiability and Query-Entailment in Forward Guarded Fragment. In: Faber, W., Friedrich, G., Gebser, M., Morak, M. (eds) Logics in Artificial Intelligence. JELIA 2021. Lecture Notes in Computer Science(), vol 12678. Springer, Cham. https://doi.org/10.1007/978-3-030-75775-5_13

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  • DOI: https://doi.org/10.1007/978-3-030-75775-5_13

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