Abstract
In this paper we investigate weak contact relations C on a lattice L, in particular, the relation between various axioms for contact, and their connection to the algebraic structure of the lattice. Furthermore, we will study a notion of orthogonality which is motivated by a weak contact relation in an inner product space. Although this is clearly a spatial application, we will show that, in case L is distributive and C satisfies the orthogonality condition, the only weak contact relation on L is the overlap relation; in particular no RCC model satisfies this condition.
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References
Cohn, A.G., Varzi, A.: Connection relations in mereotopology. In: Prade, H. (ed.) Proceedings of the 13th European Conference on Artificial Intelligence (ECAI 1998), pp. 150–154. John Wiley & Sons, Chichester (1998)
Düntsch, I., Orłowska, E.: A proof system for contact relation algebras. Journal of Philosophical Logic 29, 241–262 (2000)
Düntsch, I., Orłowska, E., Wang, H.: Algebras of approximating regions. Fundamenta Informaticae 46, 71–82 (2001)
Düntsch, I., Wang, H., McCloskey, S.: Relation algebras in qualitative spatial reasoning. Fundamenta Informaticae, 229–248 (2000)
Düntsch, I., Wang, H., McCloskey, S.: A relation algebraic approach to the Region Connection Calculus. Theoretical Computer Science 255, 63–83 (2001)
Düntsch, I., Winter, M.: A representation theorem for Boolean contact algebras. Theoretical Computer Science (B) 347, 498–512 (2005)
Eschenbach, C.: A predication calculus for qualitative spatial representation. In: [8], pp. 157–172
Freksa, C., Mark, D.M. (eds.): COSIT 1999. LNCS, vol. 1661. Springer, Heidelberg (1999)
Galton, A.: The mereotopology of discrete space. In: [8], pp. 251–266
Grätzer, G.: General Lattice Theory. Birkhäuser, Basel (1978)
Leśniewski, S.: O podstawach matematyki, 30–34 (1927–1931)
Randell, D.A., Cohn, A.G., Cui, Z.: Computing transitivity tables: A challenge for automated theorem provers. In: Kapur, D. (ed.) CADE 1992. LNCS (LNAI), vol. 607, pp. 786–790. Springer, Heidelberg (1992)
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)
Whitehead, A.N.: Process and reality. MacMillan, New York (1929)
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Düntsch, I., Winter, M. (2006). Weak Contact Structures. In: MacCaull, W., Winter, M., Düntsch, I. (eds) Relational Methods in Computer Science. RelMiCS 2005. Lecture Notes in Computer Science, vol 3929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11734673_6
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DOI: https://doi.org/10.1007/11734673_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33339-5
Online ISBN: 978-3-540-33340-1
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