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    On the decidability of connectedness constraints in 2D and 3D Euclidean spaces

    Kontchakov, Roman and Nenov, Y. and Pratt-Hartmann, I. and Zakharyaschev, Michael (2011) On the decidability of connectedness constraints in 2D and 3D Euclidean spaces. In: Walsh, T. (ed.) Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence. California, U.S.: AAAI Press, pp. 957-962. ISBN 9781577355120.

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    We investigate (quantifier-free) spatial constraint languages with equality, contact and connectedness predicates as well as Boolean operations on regions, interpreted over low-dimensional Euclidean spaces. We show that the complexity of reasoning varies dramatically depending on the dimension of the space and on the type of regions considered. For example, the logic with the interior-connectedness predicate (and without contact) is undecidable over polygons or regular closed sets in the Euclidean plane, NP-complete over regular closed sets in three-dimensional Euclidean space, and ExpTime-complete over polyhedra in three-dimensional Euclidean space.


    Item Type: Book Section
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Roman Kontchakov
    Date Deposited: 13 May 2013 08:58
    Last Modified: 09 Aug 2023 12:33


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