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A complete classification of the expressiveness of interval logics of Allen’s relations : the general and the dense cases

Aceto, Luca (author)
Della Monica, Dario (author)
Goranko, Valentin, 1959- (author)
Stockholms universitet,Filosofiska institutionen,University of Johannesburg, South Africa
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Ingólfsdóttir, Anna (author)
Montanari, Angelo (author)
Sciavicco, Guido (author)
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 (creator_code:org_t)
2015-05-14
2016
English.
In: Acta Informatica. - : Springer Science and Business Media LLC. - 0001-5903 .- 1432-0525. ; 53:3, s. 207-246
  • Journal article (peer-reviewed)
Abstract Subject headings
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  • Interval temporal logics take time intervals, instead of time points, as their primitive temporal entities. One of the most studied interval temporal logics is Halpern and Shoham’s modal logic of time intervals HS, which associates a modal operator with each binary relation between intervals over a linear order (the so-called Allen’s interval relations). In this paper, we compare and classify the expressiveness of all fragments of HS on the class of all linear orders and on the subclass of all dense linear orders. For each of these classes, we identify a complete set of definabilities between HS modalities, valid in that class, thus obtaining a complete classification of the family of all 4096 fragments of HS with respect to their expressiveness. We show that on the class of all linear orders there are exactly 1347 expressively different fragments of HS, while on the class of dense linear orders there are exactly 966 such expressively different fragments.

Subject headings

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)
NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

Keyword

Interval temporal logic
Expressiveness
Bisimulation
datalogi
Computer Science
matematisk logik
Mathematical Logic
Theoretical Philosophy
teoretisk filosofi

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ref (subject category)
art (subject category)

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