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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baader, F., Calvanese, D., MCGuinness, D., Nardi, D., Patel-Schneider, P.: The Description Logic Handbook. Cambridge University Press, Cambridge (2003)
Barlatier, P., Dapoigny, R.: A Theorem Prover with Dependent Types for Reasoning about Actions. In: Procs. of STAIRS 2008 at ECAI 2008, pp. 12–23 (2008)
Brachman, R.J., Levesque, H.J.: Knowledge Representation and Reasoning. In: Procs. of IJCAI 2004. Morgan Kaufmann, San Francisco (2004)
Bittner, T., Donnelly, M.: Computational ontologies of parthood, componenthood, and containment. In: Procs. of the Nineteenth International Joint Conference on Artificial Intelligence, pp. 382–387 (2005)
Coquand, T., Huet, G.: The calculus of constructions. Information and Computation 76(2-3), 95–120 (1988)
Dapoigny, R., Barlatier, P.: Towards a Conceptual Structure based on Type Theory. In: ICCS 2008, pp. 107–114 (2008)
Guizzardi, G., Herre, H., Wagner, G.: On the General Ontological Foundations of Conceptual Modeling. In: Spaccapietra, S., March, S.T., Kambayashi, Y. (eds.) ER 2002. LNCS, vol. 2503, pp. 65–78. Springer, Heidelberg (2002)
Harper, R., Honsell, F., Plotkin, G.: A framework for defining logics. Journal of the Association for Computing Machinery 40(1), 143–184 (1993)
Horrocks, I., Patel-Schneider, P.F.: A Proposal for an OWL Rules Language. In: Proc. of the 13th Int World Wide Web Conf. (WWW 2004). ACM, New York (2004)
Keet, C.M.: Part-Whole relations in Object-Role Models. In: 2nd Int. Workshop on Object Role Modelling (ORM 2006), Montpellier (2006)
Luo, Z.: A Unifying Theory of Dependent Types: The Schematic Approach. In: Procs. of Logical Foundations of Computer Science, pp. 293–304 (1992)
Luo, Z.: Manifest fields and module mechanisms in intensional type theory. In: Procs. of TYPES 2008 (2008)
Martin-Löf, P.: Constructive Mathematics and Computer Programming. Logic, Methodology and Philosophy of Sciences 6, 153–175 (1982)
Ferreira Pires, L., van Sinderen, M., Munthe-Kaas, E., Prokaev, S., Hutschemaekers, M., Plas, D.-J.: Techniques for describing and manipulating context information. Lucent Technologies, Freeband/A_MUSE, report D3.5v2.0 (2005)
Toninelli, A., Montanari, R., Kagal, A., Lassila, O.: A semantic Context-aware Access Control Framework for Secure Collaborations in Pervasive Computing Environments. In: Cruz, I., Decker, S., Allemang, D., Preist, C., Schwabe, D., Mika, P., Uschold, M., Aroyo, L.M. (eds.) ISWC 2006. LNCS, vol. 4273, pp. 473–486. Springer, Heidelberg (2006)
Varzi, A.C.: Parts, Wholes and Part-Whole Relations. The Prospects of Mereotopology. Data and Knowledge Engineering 20, 259–286 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dapoigny, R., Barlatier, P. (2009). Reasoning about Relations with Dependent Types: Application to Context-Aware Applications. In: Rauch, J., Raś, Z.W., Berka, P., Elomaa, T. (eds) Foundations of Intelligent Systems. ISMIS 2009. Lecture Notes in Computer Science(), vol 5722. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04125-9_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-04125-9_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04124-2
Online ISBN: 978-3-642-04125-9
eBook Packages: Computer ScienceComputer Science (R0)