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

Authors:
Richard Dapoigny;Patrick Barlatier
Affiliations:
Laboratoire d'Informatique, Systèmes, Traitement de l'Information et de la Connaissance, Université de Savoie, Annecy-le-vieux cedex, France 74944;Laboratoire d'Informatique, Systèmes, Traitement de l'Information et de la Connaissance, Université de Savoie, Annecy-le-vieux cedex, France 74944
Venue:
ISMIS '09 Proceedings of the 18th International Symposium on Foundations of Intelligent Systems
Year:
2009

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Abstract

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.