Reasoning about Relations with Dependent Types: Application to Context-Aware Applications

  • Richard Dapoigny
  • Patrick Barlatier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5722)


Generally, ontological relations are modeled using fragments of first order logic (FOL) and difficulties arise when meta-reasoning is done over ontological properties, leading to reason outside the logic. Moreover, when such systems are used to reason about knowledge and meta-knowledge, classical languages are not able to cope with different levels of abstraction in a clear and simple way. In order to address these problems, we suggest a formal framework using a dependent (higher order) type theory. It maximizes the expressiveness while preserving decidability of type checking and results in a coherent theory. Two examples of meta-reasoning with transitivity and distributivity and a case study illustrate this approach.


Description Logic Type Theory First Order Logic Dependent Type Stop Time 
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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Richard Dapoigny
    • 1
  • Patrick Barlatier
    • 1
  1. 1.Laboratoire d’Informatique, Systèmes, Traitement de l’Information et de la ConnaissanceUniversité de SavoieAnnecy-le-vieux cedexFrance

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