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Time-Dependent Contact Structures in Goguen Categories

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Relational Methods in Computer Science (RelMiCS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3929))

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Abstract

In this paper we focus on a theory of time-extended contact. It turns out that a suitable theory can be defined using an \(\mathcal{L}\)-valued or \(\mathcal{L}\)-fuzzy version of a contact relation. We study this structure in the context of Goguen categories – a suitable categorical formalization of \(\mathcal{L}\)-valued or \(\mathcal{L}\)-fuzzy relations.

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References

  1. Biacino, L., Gerla, G.: Connection Structures. Notre Dame Journal of Formal Logic 32, 242–247 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  2. Clarke, B.L.: A calculus of individuals based on ‘connenction’. Notre Dame Journal of Formal Logic 22, 204–218 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  3. Düntsch, I., Winter, M.: Finite Contact Structure. In: MacCaull, W., Winter, M., Düntsch, I. (eds.) RelMiCS 2005. LNCS, vol. 3929. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  4. Freyd, P., Scedrov, A.: Categories, Allegories. North-Holland, Amsterdam (1990)

    MATH  Google Scholar 

  5. Furusawa, H.: Algebraic Formalisations of Fuzzy Relations and their Representation Theorems. Ph.D-Thesis, Department of Informatics, Kyushu University, Japan (1998)

    Google Scholar 

  6. Goguen, J.A.: L-fuzzy sets. J. Math. Anal. Appl. 18, 145–157 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kawahara, Y., Furusawa, H.: Crispness and Representation Theorems in Dedekind Categories. DOI-TR 143, Kyushu University (1997)

    Google Scholar 

  8. Kawahara, Y., Furusawa, H.: An Algebraic Formalization of Fuzzy Relations. Fuzzy Sets and Systems 101, 125–135 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. Leonard, H.S., Goodman, N.: The calculus of individuals and its use. Journal of Symbolic Logic 5, 45–55 (1940)

    Article  MathSciNet  MATH  Google Scholar 

  10. Olivier, J.P., Serrato, D.: Catégories de Dedekind. Morphismes dans les Catégories de Schröder. C.R. Acad. Sci. Paris 290, 939–941 (1980)

    MATH  Google Scholar 

  11. Olivier, J.P., Serrato, D.: Squares and Rectangles in Relational Categories - Three Cases: Semilattice, Distributive lattice and Boolean Non-unitary. Fuzzy sets and systems 72, 167–178 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  12. 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)

    Google Scholar 

  13. Schmidt, G., Ströhlein, T.: Relationen und Graphen. Springer, Heidelberg (1989); English version: Relations and Graphs. Discrete Mathematics for Computer Scientists, EATCS Monographs on Theoret. Comput. Sci. Springer, Heidelberg (1993)

    Book  MATH  Google Scholar 

  14. Schmidt, G., Hattensperger, C., Winter, M.: Heterogeneous Relation Algebras. In: Brink, C., Kahl, W., Schmidt, G. (eds.) Relational Methods in Computer Science. Advances in Computer Science. Springer, Vienna (1997)

    Google Scholar 

  15. Stell, J.: Boolean connection algebras: A new approach to the Region Connection Calculus. Artificial Intelligence 122, 111–136 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  16. Winter, M.: Strukturtheorie heterogener Relationenalgebren mit Anwendung auf Nichtdetermismus in Programmiersprachen. Dissertationsverlag NG Kopierladen GmbH, München (1998)

    Google Scholar 

  17. Winter, M.: A new Algebraic Approach to L-Fuzzy Relations convenient to study Crispness. Information Sciences 139, 233–252 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Winter, M.: Derived Operations in Goguen Categories. Theory and Applications of Categories 10, 220–247 (2002)

    MathSciNet  MATH  Google Scholar 

  19. Winter, M.: Relational Constructions in Goguen Categories. In: de Swart, H. (ed.) RelMiCS 2001. LNCS, vol. 2561, pp. 212–227. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  20. Winter, M.: Representation Theory of Goguen Categories. Fuzzy Sets and Systems 138, 85–126 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  21. Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Brock University, St.Catharines, Ontario, L2S 3A1, Canada

    Michael Winter

Authors
  1. Michael Winter
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, NS, Canada

    Wendy MacCaull

  2. Department of Computer Science, Brock University, L2S 3A1, St. Catharines, Ontario, Canada

    Michael Winter

  3. Computer Science Department, Brock University, L2S 3A1, St. Catharines, Ontario, Canada

    Ivo Düntsch

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© 2006 Springer-Verlag Berlin Heidelberg

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Winter, M. (2006). Time-Dependent Contact Structures in Goguen Categories. 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_20

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  • DOI: https://doi.org/10.1007/11734673_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33339-5

  • Online ISBN: 978-3-540-33340-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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