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The Time Ontology of Allen's Interval Algebra

Authors Michael Grüninger, Zhuojun Li



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Michael Grüninger
Zhuojun Li

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Michael Grüninger and Zhuojun Li. The Time Ontology of Allen's Interval Algebra. In 24th International Symposium on Temporal Representation and Reasoning (TIME 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 90, pp. 16:1-16:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.TIME.2017.16

Abstract

Allen's interval algebra is a set of thirteen jointly exhaustive and pairwise disjoint binary relations representing temporal relationships between pairs of timeintervals. Despite widespread use, there is still the question of which time ontology actually underlies Allen's algebra. Early work specified a first-order ontology that can interpret Allen's interval algebra; in this paper, we identify the first-order ontology that is logically synonymous with Allen's interval algebra, so that there is a one-to-one correspondence between models of the ontology and solutions to temporal constraints that are specified using the temporal relations. We further prove a representation theorem for the ontology, thus characterizing its models up to isomorphism.
Keywords
  • time ontology
  • intervals
  • composition table
  • first-order logic
  • synonymy

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