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Allen’s Interval Algebra Makes the Difference

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Declarative Programming and Knowledge Management (INAP 2019, WLP 2019, WFLP 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12057))

Abstract

Allen’s Interval Algebra constitutes a framework for reasoning about temporal information in a qualitative manner. In particular, it uses intervals, i.e., pairs of endpoints, on the timeline to represent entities corresponding to actions, events, or tasks, and binary relations such as precedes and overlaps to encode the possible configurations between those entities. Allen’s calculus has found its way in many academic and industrial applications that involve, most commonly, planning and scheduling, temporal databases, and healthcare. In this paper, we present a novel encoding of Interval Algebra using answer-set programming (ASP) extended by difference constraints, i.e., the fragment abbreviated as ASP(DL), and demonstrate its performance via a preliminary experimental evaluation. Although our ASP encoding is presented in the case of Allen’s calculus for the sake of clarity, we suggest that analogous encodings can be devised for other point-based calculi, too.

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Notes

  1. 1.

    This distinguished variable z can be used as a name for 0 in other difference constraints. Then, e.g., \(x-z\le k\) and \(z-x\le -k\) express together that \(x=k\).

  2. 2.

    https://potassco.org/labs/clingodl/.

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Acknowledgments

This research was partially supported by the project Ethical AI for the Governance of Society (ETAIROS, grant #327352) funded by the Academy of Finland.

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Authors and Affiliations

  1. Department of Computer Science, Aalto University, Espoo, Finland

    Tomi Janhunen & Michael Sioutis

  2. Computing Sciences Unit, Tampere University, Tampere, Finland

    Tomi Janhunen

Authors
  1. Tomi Janhunen
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  2. Michael Sioutis
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Corresponding author

Correspondence to Tomi Janhunen .

Editor information

Editors and Affiliations

  1. Brandenburgische Technische Universität Cottbus-Senftenberg, Cottbus, Germany

    Petra Hofstedt

  2. Universidade de Évora, Évora, Portugal

    Salvador Abreu

  3. hwtk Berlin, Berlin, Germany

    Ulrich John

  4. Westfälische Wilhelms-Universität Münster, Münster, Germany

    Herbert Kuchen

  5. Universität Würzburg, Würzburg, Germany

    Dietmar Seipel

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Janhunen, T., Sioutis, M. (2020). Allen’s Interval Algebra Makes the Difference. In: Hofstedt, P., Abreu, S., John, U., Kuchen, H., Seipel, D. (eds) Declarative Programming and Knowledge Management. INAP WLP WFLP 2019 2019 2019. Lecture Notes in Computer Science(), vol 12057. Springer, Cham. https://doi.org/10.1007/978-3-030-46714-2_6

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  • DOI: https://doi.org/10.1007/978-3-030-46714-2_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-46713-5

  • Online ISBN: 978-3-030-46714-2

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