A modal approach to dynamic ontology: modal mereotopology

Dimiter Vakarelov

DOI: http://dx.doi.org/10.12775/LLP.2008.010

Abstract


In this paper we show how modal logic can be applied in the axiomatizations of some dynamic ontologies. As an example we consider the case of mereotopology, which is an extension of mereology with some relations of topological nature like contact relation. We show that in the modal extension of mereotopology we may define some new mereological and mereotopological relations with dynamic nature like stable part-of and stable contact. In some sense such “stable” relations can be considered as approximations of the “essential relations” in the domain of mereotopology.

Keywords


ontology; dynamic ontology; mereology; mereotopology; modal logic; essential relations

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References


Aiello, M., I. Pratt, and J. van Benthem (eds.), Handbook of Spatial Logics, Springer, 2007.

Balbiani, Ph., T. Tinchev, and D. Vakarelov, “Modal logics for region-based theory of space”, Fundamenta Informaticae 81, 1–3 (2007), 29–82.

Bennett, B., and I. Duentsch, “Axioms, algebras and topology”, in [1].

de Laguna, T., “Point, line and surface as sets of solids”, The Journal of Philosophy 19 (1922), 449–461.

Dimov, G., and D. Vakarelov, “Contact algebras and region-based theory of space: a proximity approach. I, II”, Fundamenta Informaticae 74 (2006), 209–282.

Düntsch, I., and M. Winter, “A representation theorem for Boolean Contact Algebras”, Theoretical Computer Science (B) 347 (2005), 498–512.

Fine, K., “Essence and modality”, pp. 1–16 in J. Tomberlin (ed.) Philosophical Perspective 8, 1994.

Hughes, G.E., and M.J. Cresswell, A New Introduction to Madal Logic, Routledge, London and New York, 1996.

Konchakov, R., A. Kurucz, F. Wolter, and M. Zakharyaschev, “Spatial Logic + Temporal Logic = ?”, in [1].

Pratt-Hartmann, I., “First-order region-based theories of space”, in [1].

Simons, P., Parts. A Study in Ontology, Oxford, Clarendon Press, 1987.

Whitehead, A.N., Process and Reality, New York, MacMillan, 1929.

Vakarelov, D., “Region-based theory of space: algebras of regions, representation theory and logics”, pp. 267–348 in Dov Gabbay et al. (eds.), Mathematical Problems from Applied Logics, “New Logics for the XXIst Century. II”, Springer, 2007.

Wolter, F., and M. Zakharyaschev, “Spatial representation and reasoning in RCC-8 with Boolean region terms”, pp. 244–248 in W. Horn (ed.), Proceedings of the 14th European Conference on Artificial Intelligence (ECAI 2000), IOS Press.








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