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A Connection between Clone Theory and FCA Provided by Duality Theory

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 7278)

Abstract

The aim of this paper is to show how Formal Concept Analysis can be used for the benefit of clone theory. More precisely, we show how a recently developed duality theory for clones can be used to dualize clones over bounded lattices into the framework of Formal Concept Analysis, where they can be investigated with techniques very different from those that universal algebraists are usually armed with. We also illustrate this approach with some small examples.

Keywords

  • clones
  • duality theory
  • Formal Concept Analysis
  • clones of dual operations
  • coclones
  • bounded lattices
  • standard topological contexts

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References

  1. Csákány, B.: Completeness in coalgebras. Acta Sci. Math. 48, 75–84 (1985)

    MATH  Google Scholar 

  2. Gowers, T., Barrow-Green, J., Leader, I. (eds.): The Princeton companion to mathematics. Princeton University Press, Princeton (2008)

    MATH  Google Scholar 

  3. Gehrke, M.: Generalized Kripke frames. Studia Logica 84(2), 241–275 (2006)

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Ganter, B., Wille, R.: Formal concept analysis. Mathematical foundations. Springer, Berlin (1999); Translated from the 1996 German original by Cornelia Franzke

    Google Scholar 

  5. Hartung, G.: An extended duality for lattices. In: General Algebra and Applications, Potsdam. Res. Exp. Math., vol. 20, pp. 126–142. Heldermann, Berlin (1992, 1993)

    Google Scholar 

  6. Hazewinkel, M. (ed.): Encyclopaedia of mathematics. A–Zyg, index, vol. 1–6. Kluwer Academic Publishers, Dordrecht (1995); Translated from the Russian, Reprint of the 1988-1994 English translation

    Google Scholar 

  7. Hartonas, C., Dunn, J.M.: Stone duality for lattices. Algebra Universalis 37(3), 391–401 (1997)

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Kerkhoff, S.: A general duality theory for clones, Ph.D. thesis, Technische Universität Dresden (2011)

    Google Scholar 

  9. Mašulović, D.: On dualizing clones as lawvere theories. International Journal of Algebra and Computation 16, 675–687 (2006)

    Google Scholar 

  10. McKenzie, R.: Finite forbidden lattices. In: Universal Algebra and Lattice Theory, Puebla. Lecture Notes in Math., vol. 1004, pp. 176–205. Springer, Berlin (1982, 1983)

    Google Scholar 

  11. McKenzie, R.N., McNulty, G.F., Taylor, W.: Algebras, lattices, varieties. The Wadsworth & Brooks/Cole Mathematics, vol. I. Wadsworth & Brooks/Cole Advanced Books & Software, Monterey (1987)

    MATH  Google Scholar 

  12. Urquhart, A.: A topological representation theory for lattices. Algebra Universalis 8(1), 45–58 (1978)

    CrossRef  MathSciNet  MATH  Google Scholar 

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Kerkhoff, S. (2012). A Connection between Clone Theory and FCA Provided by Duality Theory. In: Domenach, F., Ignatov, D.I., Poelmans, J. (eds) Formal Concept Analysis. ICFCA 2012. Lecture Notes in Computer Science(), vol 7278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29892-9_17

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  • DOI: https://doi.org/10.1007/978-3-642-29892-9_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29891-2

  • Online ISBN: 978-3-642-29892-9

  • eBook Packages: Computer ScienceComputer Science (R0)