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Trends in Temporal Reasoning: Constraints, Graphs and Posets

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Mathematical Aspects of Computer and Information Sciences (MACIS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9582))

Abstract

Temporal reasoning finds many applications in numerous fields of artificial intelligence – frameworks for representing and analyzing temporal information are therefore important. Allen’s interval algebra is a calculus for temporal reasoning that was introduced in 1983. Reasoning with qualitative time in Allen’s full interval algebra is NP-complete. Research since 1995 identified maximal tractable subclasses of this algebra via exhaustive computer search and also other ad-hoc methods. In 2003, the full classification of complexity for satisfiability problems over constraints in Allen’s interval algebra was established algebraically. We review temporal reasoning concepts including a method for deciding tractability of temporal constraint satisfaction problems based on the theory of algebraic closure operators for constraints. Graph-based temporal representations such as interval and sequence graphs are discussed. We also propose novel research for scheduling algorithms based on the Fishburn-Shepp inequality for posets.

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Notes

  1. 1.

    Throughout we assume \(P \ne NP\).

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Author information

Authors and Affiliations

  1. Department of Computer Science, Royal Holloway, University of London, Egham, UK

    Jacqueline W. Daykin

  2. Department of Informatics, King’s College London, London, UK

    Jacqueline W. Daykin

  3. School of Electrical Engineering and Computer Science, University of Newcastle, New South Wales, Australia

    Mirka Miller & Joe Ryan

  4. Department of Mathematics, University of West Bohemia, Pilsen, Czech Republic

    Mirka Miller

Authors
  1. Jacqueline W. Daykin
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  2. Mirka Miller
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Correspondence to Jacqueline W. Daykin .

Editor information

Editors and Affiliations

  1. Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  2. Hamburg University of Technology, Hamburg, Germany

    Siegfried M. Rump

  3. New York University, New York, New York, USA

    Chee K. Yap

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Daykin, J.W., Miller, M., Ryan, J. (2016). Trends in Temporal Reasoning: Constraints, Graphs and Posets. In: Kotsireas, I., Rump, S., Yap, C. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2015. Lecture Notes in Computer Science(), vol 9582. Springer, Cham. https://doi.org/10.1007/978-3-319-32859-1_25

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  • DOI: https://doi.org/10.1007/978-3-319-32859-1_25

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