Abstract
We show that the class of Boolean contact algebras has the joint embedding property and the amalgamation property, and that the class of connected Boolean contact algebras has the joint embedding property but not the amalgamation property.
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Aiello, M., Pratt-Hartmann, I., van Benthem, J. (eds.): Handbook of Spatial Logics. Springer, Dordrecht (2007)
Bennett, B., Düntsch, I.: Algebras, axioms, and topology. In: Aiello, et al. [1], pp. 99–159
Bodirsky, M., Wölfl, S.: RCC8 is polynomial on networks of bounded treewidth. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence, pp. 756–761 (2011)
Dimov, G., Vakarelov, D.: Contact algebras and region–based theory of space: A proximity approach – I, II. Fundamenta Informaticae 74, 209–282 (2006)
Düntsch, I., Li, S.: On the homogeneous countable Boolean contact algebra (2012) (preprint)
Düntsch, I., Vakarelov, D.: Region–based theory of discrete spaces: A proximity approach. Annals of Mathematics and Artificial Intelligence 49, 5–14 (2007)
Düntsch, I., Winter, M.: The Lattice of Contact Relations on a Boolean Algebra. In: Berghammer, R., Möller, B., Struth, G. (eds.) RelMiCS/AKA 2008. LNCS, vol. 4988, pp. 99–109. Springer, Heidelberg (2008)
Galton, A.: The Mereotopology of Discrete Space. In: Freksa, C., Mark, D.M. (eds.) COSIT 1999. LNCS, vol. 1661, pp. 251–266. Springer, Heidelberg (1999)
Hodges, W.: Model theory. Cambridge University Press, Cambridge (1993)
Jónsson, B.: Maximal algebras of binary relations. Contemporary Mathematics 33, 299–307 (1984)
Koppelberg, S.: General Theory of Boolean Algebras. In: Handbook of Boolean Algebras, vol. 1. North–Holland (1989)
Li, S., Ying, M.: Generalized Region Connection Calculus. Artificial Intelligence 160(1-2), 1–34 (2004)
Li, Y., Li, S., Ying, M.: Relational reasoning in the region connection calculus (2003), http://arxiv.org/abs/cs.AI/0505041
Madarász, J., Sayed Ahmed, T.: Amalgamation, interpolation and epimorphisms in alegraic logic. In: Andréka, H., Ferenczi, M., Németi, I. (eds.) Cylindric–like Algebras and Algebraic Logic, Bolay Society Mathematical Studies, vol. 22, pp. 65–77. North–Holland (2012)
Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connection. In: Nebel, B., Swartout, W., Rich, C. (eds.) Proceedings of the 3rd International Conference on Knowledge Representation and Reasoning, pp. 165–176. Morgan Kaufmann (1992)
Renz, J., Nebel, B.: Qualitative spatial reasoning using constraint calculi. In: Aiello, et al. [1], pp. 161–215
Sabidussi, G.: Graph multiplication. Mathematische Zeitschrift 72(1), 446–457 (1959)
Stell, J.: Boolean connection algebras: A new approach to the Region Connection Calculus. Artificial Intelligence 122, 111–136 (2000)
Vakarelov, D., Dimov, G., Düntsch, I., Bennett, B.: A proximity approach to some region–based theories of space. J. Appl. Non-Classical Logics 12, 527–529 (2002)
Weichsel, P.M.: The Kronecker Product of Graphs. Proceedings of the American Mathematical Society 13, 47–52 (1962)
Wolter, F., Zakharyaschev, M.: Spatial reasoning in RCC-8 with Boolean region terms. In: Horn, W. (ed.) ECAI, pp. 244–250. IOS Press (2000)
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Düntsch, I., Li, S. (2012). Extension Properties of Boolean Contact Algebras. In: Kahl, W., Griffin, T.G. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2012. Lecture Notes in Computer Science, vol 7560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33314-9_23
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DOI: https://doi.org/10.1007/978-3-642-33314-9_23
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