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Using temporal constraints for temporal abstraction

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Abstract

The need to provide high level descriptions of the evolution of data is evident in fields like medicine. For being able to perform task such as diagnostic or monitoring, it is very important to facilitate a high level representation and management of temporal data. With this representation two main benefits are obtained: it becomes easier to compare data with generic knowledge, and the volume of data can be reduced. Several models have been proposed for time representation and management. Temporal constraints have been extensively used as a liable model in problems where temporal imprecision or missing data exist. The imprecision is usually present when data are manually collected, or when the data are based on subjective observations. The aim of this paper is to demonstrate how temporal constraints can be used as a formalism in which temporal abstraction of concepts can be performed. To this end, in the first place, we introduce the fuzzy temporal constraint network as the formalism for representing temporal information. Then, we present an algorithm for obtaining a state representation from a sequence of observations. We show the complexity and applicability of the approach.

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Notes

  1. Where m and s represent minutes and seconds, respectively.

  2. Where m and s represent minutes and seconds, respectively.

  3. We have defined in Campos et al. (2005) a series of basic abstractions (qualitative, generalizations, etc) which can be expressed in this way.

  4. Given a temporal network \(\mathcal{N}=\langle\mathcal{T},\mathcal{L}\rangle\), the symbol ≺ will represent a binary relation in the set of temporal variables \(\mathcal{L}\), \(\prec\subseteq\mathcal{T}\times\mathcal{T}\) defined as \(T_{i}\prec T_{j}\leftrightarrow\mathcal{L}(T_{i},T_{j})\subseteq\mathcal{L}^{+}\).

  5. A network in which the ≺ relation is a total order is called an ordered network.

  6. As explained in Section 2, we use a discrete representation of time.

  7. The operation \(g_{p}\oplus\mathcal{L}^{+}\) is a fuzzyfication of the granularity. Since this is a whole number and is composed with the positive constraint \(\mathcal{L}^{+}\), we obtain a fuzzy constraint corresponding to L(g p , + ∞ ).

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Authors and Affiliations

  1. Informatics and Systems Dept., Computer Science faculty, University of Murcia, Murcia, Spain

    M. Campos

  2. Information and Communications Engineering Dept., Computer Science faculty, University of Murcia, Murcia, Spain

    J. M. Juárez, J. Palma & R. Marín

Authors
  1. M. Campos
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  2. J. M. Juárez
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  3. J. Palma
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  4. R. Marín
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Corresponding author

Correspondence to M. Campos.

Additional information

This work was supported by the Spanish Ministry of Education and Science(MEC) and the European Regional Development Fund of the European Commission(FEDER) under grants TIN2006-15460-C04-01 and PET2006-0406 and the Regional Agency for Science and Technology (Seneca Foundation) under grant 08853/PI/08.

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Campos, M., Juárez, J.M., Palma, J. et al. Using temporal constraints for temporal abstraction. J Intell Inf Syst 34, 57–92 (2010). https://doi.org/10.1007/s10844-009-0079-6

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