Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Allen’s Relations

  • Peter Revesz
  • Paolo Terenziani
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_1515

Synonyms

Qualitative relations between time intervals; Qualitative temporal constraints between time intervals

Definition

A (convex) time interval I is the set of all time points between a starting point (usually denoted by I ) and an ending point (I +). Allen’s relations model all possible relative positions between two time intervals [ 1]. There are 13 different possibilities, depending on the relative positions of the endpoints of the intervals (Table  1).
Allen’s Relations, Table 1

Translation of Allen’s interval relations between two intervals I and J into conjunctions of point relations between I−, I+, J−, and J+

 

I J

I J+

I+J

I+ J+

After

 

>

   

Before

   

<

 

Meets

   

=

 

Met_by

 

=

   

During

>

   

<

Contains

<

   

>

Equal

=

   

=

Finishes

>

   

=

Finished_by

<

   

=

Starts

=

   

<

Started_by

=

   

>

Overlaps

<

 

>

<

Overlapped_by

>

<

 

>

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Recommended Reading

  1. 1.
    Allen JF. Maintaining knowledge about temporal intervals. Commun ACM. 1983;26(11):832–43.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of Nebraska-LincolnLincolnUSA
  2. 2.Dipartimento di Scienze e Innovazione Tecnologica (DiSIT)Università del Piemonte Orientale, "Amedeo Avogadro"AlessandriaItaly

Section editors and affiliations

  • Richard T. Snodgrass
    • 1
  • Christian S. Jensen
    • 2
  1. 1.University of ArizonaTucsonUSA
  2. 2.Aalborg UniversityAalborg ØstDenmark