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Contact Relations with Applications

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Relations and Kleene Algebra in Computer Science (RelMiCS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5827))

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Abstract

Using relation algebra, we generalize Aumann’s notion of a contact relation and that of a closure operation from powersets to general membership relations and their induced partial orders. We also investigate the relationship between contacts and closures in this general setting and use contacts to establish a one-to-one correspondence between the column space and the row space of a relation.

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References

  1. Aumann, G.: Kontaktrelationen. Bayerische Akademie der Wissenschaften. Mathematisch-Naturwissenschaftliche Klasse Sitzungsberichte 1970, 67–77 (1970)

    Google Scholar 

  2. Berghammer, R.: Relation-algebraic computation of fixed points with applications. Journal of Logic and Algebraic Programming 66, 112–126 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Berghammer, R., Neumann, F.: RelView – An OBDD-Based Computer Algebra System for Relations. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2005. LNCS, vol. 3718, pp. 40–51. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Berghammer, R., Schmidt, G., Zierer, H.: Symmetric quotients. Report TUM-I8620, Institut für Informatik, Technische Universität München (1986)

    Google Scholar 

  5. Berghammer, R., Schmidt, G., Zierer, H.: Symmetric quotients and domain constructions. Information Processing Letters 33, 163–168 (1989/1990)

    Article  MATH  MathSciNet  Google Scholar 

  6. Caspard, N., Monjardet, B.: The lattices of closure systems, closure operators, and implicational systems on a finite set: a survey. Discrete Applied Mathematics 127, 241–269 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Doignon, J.P., Falmagne, J.C.: Knowledge spaces. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  8. Düntsch, I., Winter, M.: A representation theorem for Boolean contact algebras. Theoretical Computer Science B 347, 498–512 (2005)

    Article  MATH  Google Scholar 

  9. Ganter, B., Wille, R.: Formal concept analysis. Mathematical foundations. Springer, Heidelberg (1998)

    Google Scholar 

  10. Private communication with P. Jipsen (2008)

    Google Scholar 

  11. Kim, K.H.: Boolean matrix theory and applications. Marcel Dekker, New York (1982)

    MATH  Google Scholar 

  12. Schmidt, G., Ströhlein, T.: Relationen und Graphen. Springer, Heidelberg (1989). Available also in English: Relations and graphs. Discrete Mathematics for Computer Scientists. EATCS Monographs on Theoretical Computer Science (1993)

    Google Scholar 

  13. Tarski, A.: On the calculus of relations. Journal of Symbolic Logic 6, 73–89 (1941)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Fakultät für Informatik, Universität der Bundeswehr München, 85577, Neubiberg, Germany

    Gunther Schmidt

  2. Institut für Informatik, Christian-Albrechts-Universität Kiel, Olshausenstraße 40, 24098, Kiel, Germany

    Rudolf Berghammer

Authors
  1. Gunther Schmidt
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  2. Rudolf Berghammer
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität zu Kiel, Olshausenstraße 40, 24098, Kiel, Germany

    Rudolf Berghammer

  2. College of Engineering, Qatar University, P.O. Box 2713, CSE 209, Doha, Qatar,  

    Ali Mohamed Jaoua

  3. Institut für Informatik, Universität Augsburg, Universitätsstr. 6a, 86135, Augsburg, Germany

    Bernhard Möller

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© 2009 Springer-Verlag Berlin Heidelberg

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Schmidt, G., Berghammer, R. (2009). Contact Relations with Applications. In: Berghammer, R., Jaoua, A.M., Möller, B. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2009. Lecture Notes in Computer Science, vol 5827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04639-1_21

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  • DOI: https://doi.org/10.1007/978-3-642-04639-1_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04638-4

  • Online ISBN: 978-3-642-04639-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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