Nicolas Markey

Résumé

A chronicle is a temporal model introduced by Dousson et al. for situation recognition. In short, a chronicle consists of a set of events and a set of real-valued temporal constraints on the delays between pairs of events. This work investigates the relationship between chronicles and classical temporal model formalisms, namely TPTL and MTL. More specifically, we answer the following question: is it possible to find an equivalent formula in such formalisms for any chronicle? This question arises from the observation that a single chronicle captures complex temporal behaviours that do not order the events in time.

In this article, we introduce the subclass of linear chronicles, which defines a temporal order of occurrence of the event to be recognized in a temporal sequence. Our first result is that any chronicle can be expressed as a disjunction of linear chronicles. Our second result is that any linear chronicle has an equivalent TPTL formula. Using existing expressiveness results between TPTL and MTL, we show that some chronicles have no equivalent in MTL. This confirms that the model of chronicle has interesting properties for situation recognition.

@inproceedings{time2022-GM,
  author =              {Guyet, {\relax Th}omas and Markey, Nicolas},
  title =               {Logical forms of chronicles},
  editor =              {Artikis, Alexander and Posenato, Roberto and
                         Tonetta, Stefano},
  booktitle =           {{P}roceedings of the 29th {I}nternational
                         {S}ymposium on {T}emporal {R}epresentation and
                         {R}easoning ({TIME}'22)},
  acronym =             {{TIME}'22},
  publisher =           {Leibniz-Zentrum f{\"u}r Informatik},
  series =              {Leibniz International Proceedings in Informatics},
  pages =               {7:1-7:15},
  year =                {2022},
  month =               nov,
  doi =                 {10.4230/LIPIcs.TIME.2022.7},
  abstract =            {A~chronicle is a temporal model introduced by
                         Dousson~\textit{et~al.} for situation recognition.
                         In~short, a chronicle consists of a set of events
                         and a set of real-valued temporal constraints on the
                         delays between pairs of events. This~work
                         investigates the relationship between chronicles and
                         classical temporal model formalisms, namely
                         \textsf{TPTL} and~\textsf{MTL}. More~specifically,
                         we~answer the following question: is~it possible to
                         find an equivalent formula in such formalisms for
                         any chronicle? This~question arises from the
                         observation that a single chronicle captures complex
                         temporal behaviours that do not order the events in
                         time.\par In~this article, we~introduce the subclass
                         of linear chronicles, which defines a temporal order
                         of occurrence of the event to be recognized in a
                         temporal sequence. Our~first result is that any
                         chronicle can be expressed as a disjunction of
                         linear chronicles. Our~second result is that any
                         linear chronicle has an equivalent \textsf{TPTL}
                         formula. Using existing expressiveness results
                         between \textsf{TPTL} and~\textsf{MTL}, we~show that
                         some chronicles have no equivalent in~\textsf{MTL}.
                         This confirms that the model of chronicle has
                         interesting properties for situation recognition.},
}