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Convex solutions of RCC8 networks

Schockaert, Steven ORCID: and Li, Sanjiang 2014. Convex solutions of RCC8 networks. Presented at: 20th European Conference on Artificial Intelligence (ECAI 2012), Montpellier, France, 27-31 August 2012. Published in: De Raedt, Luc, Bessiere, Christian, Dubois, Didier, Doherty, Patrick, Frasconi, Paolo, Heinz, Fredrik and Lucas, Peter eds. Ecai 2012: 20th European Conference on Artificial Intelligence. Frontiers in Artificial Intelligence and Applications (242) IOS Press, pp. 726-731. 10.3233/978-1-61499-098-7-726

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RCC8 is one of the most widely used calculi for qualitative spatial reasoning. Although many applications have been explored where RCC8 relations refer to geographical or physical regions in two- or three-dimensional spaces, their use for conceptual reasoning is still at a rather preliminary stage. One of the core obstacles with using RCC8 to reason about conceptual spaces is that regions are required to be convex in this context. We investigate in this paper how the latter requirement impacts the realizability of RCC8 networks. Specifically, we show that consistent RCC8 networks over 2n + 1 variables are guaranteed to have a convex solution in Euclidean spaces of n dimensions and higher. We furthermore prove that our bound is optimal for 2- and 3-dimensional spaces, and that for any number of dimensions n ≥ 4, there exists a network of RCC8 relations over 3n variables which is consistent, but does not allow a convex solution in the n-dimensional Euclidean space.

Item Type: Conference or Workshop Item (Paper)
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Publisher: IOS Press
ISBN: 9781614990970
Last Modified: 27 Oct 2022 10:01

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