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Preconcept Algebras and Generalized Double Boolean Algebras

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Concept Lattices (ICFCA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2961))

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Abstract

Boolean Concept Logic as an integrated generalization of Contextual Object Logic and Contextual Attribute Logic can be substantially developed on the basis of preconcept algebras. The main results reported in this paper are the Basic Theorem on Preconcept Algebras and the Theorem characterizing the equational class generated by all preconcept algebras by the equational axioms of the generalized double Boolean algebras.

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References

  1. Boole, G.: An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities. Macmillan, Basingstoke (1854); Reprinted by Dover Publ., New York (1958)

    Google Scholar 

  2. Dau, F., Klinger, J.: From Formal Concept Analysis to Contextual Logic. FB4-Preprint, TU Darmstadt (2003)

    Google Scholar 

  3. Davey, B.A., Priestley, H.: Introduction to lattices and order. Cambridge University Press, Cambridge (1990)

    MATH  Google Scholar 

  4. Ganter, B., Wille, R.: Formal Concept Analysis: mathematical foundations. Springer, Heidelberg (1999); German version: Springer, Heidelberg (1996)

    MATH  Google Scholar 

  5. Ganter, B., Wille, R.: Contextual Attribute Logic. In: Tepfenhart, W., Cyre, W. (eds.) ICCS 1999. LNCS (LNAI), vol. 1640, pp. 377–388. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  6. Herrmann, C., Luksch, P., Skorsky, M., Wille, R.: Algebras of semiconcepts and double Boolean algebras. In: Contributions to General Algebra, vol. 13, pp. 175–188. Verlag Johannes Heyn, Klagenfurt (2001)

    Google Scholar 

  7. Klinger, J., Vormbrock, B.: Contextual Boolean Logic: how did it develop? In: Ganter, B., de Moor, A. (eds.) Using conceptual structures. Contributions to ICCS 2003, pp. 143–156. Shaker Verlag, Aachen (2003)

    Google Scholar 

  8. Luksch, P., Wille, R.: A mathematical model for conceptual knowledge systems. In: Bock, H.H., Ihm, P. (eds.) Classification, data analysis, and knowledge organisation, pp. 156–162. Springer, Heidelberg (1991)

    Google Scholar 

  9. Schröder, E.: Algebra der Logik, Bd. 1. Leipzig (1890); published again by Chelsea Publ. Comp., New York (1966)

    Google Scholar 

  10. Seiler, T.B.: Begreifen und Verstehen. Ein Buch über Begriffe und Bedeutungen. Verlag Allgemeine Wissenschaft, Mühltal (2001)

    Google Scholar 

  11. Stahl, J., Wille, R.: Preconcepts and set representations of contexts. In: Gaul, W., Schader, M. (eds.) Classification as a tool of research, pp. 431–438. North- Holland, Amsterdam (1986)

    Google Scholar 

  12. Vormbrock, B., Wille, R.: Semiconcept and protoconcept algebras: the basic theorems. FB4-Preprint, TU Darmstadt (2003)

    Google Scholar 

  13. Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered sets, pp. 445–470. Reidel, Dordrecht (1982)

    Google Scholar 

  14. Wille, R.: Concept lattices and conceptual knowledge systems. Computers & Mathematics with Applications 23, 493–515 (1992)

    Article  MATH  Google Scholar 

  15. Wille, R.: Plädoyer für eine philosophische Grundlegung der Begrifflichen Wissensverarbeitung. In: Wille, R., Zickwolff, M. (eds.) Begriffliche Wissensverarbeitung Grundfragen und Aufgaben, pp. 11–25. B.I.-Wissenschaftsverlag, Mannheim (1994)

    Google Scholar 

  16. Wille, R.: Restructuring mathematical logic: an approach based on Peirce’s pragmatism. In: Ursini, A., Agliano, P. (eds.) Logic and Algebra, pp. 267–281. Marcel Dekker, New York (1996)

    Google Scholar 

  17. Wille, R.: Boolean Concept Logic. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS (LNAI), vol. 1867, pp. 317–331. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  18. Wille, R.: Contextual Logic summary. In: Stumme, G. (ed.) Working with Conceptual Structures. Contributions to ICCS, pp. 265–276. Shaker, Aachen (2000)

    Google Scholar 

  19. Wille, R.: Boolean Judgment Logic. In: Delugach, H.S., Stumme, G. (eds.) ICCS 2001. LNCS (LNAI), vol. 2120, pp. 115–128. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  20. Wille, R.: Conceptual content as information - basics for Conceptual Judgment Logic. In: Ganter, B., de Moor, A., Lex, W. (eds.) ICCS 2003. LNCS (LNAI), vol. 2746, pp. 1–15. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  21. Wille, R.: Formal Concept Analysis as mathematical theory of concepts and concept hierarchies. FB4-Preprint, TU Darmstadt (2003)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstr. 7, D–64289, Darmstadt

    Rudolf Wille

Authors
  1. Rudolf Wille
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Editor information

Editors and Affiliations

  1. School of Information Systems and Technology, University of Wollongong, Northfields Ave, NSW 2522, Wollongong, Australia

    Peter Eklund

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Wille, R. (2004). Preconcept Algebras and Generalized Double Boolean Algebras. In: Eklund, P. (eds) Concept Lattices. ICFCA 2004. Lecture Notes in Computer Science(), vol 2961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24651-0_1

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  • DOI: https://doi.org/10.1007/978-3-540-24651-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21043-6

  • Online ISBN: 978-3-540-24651-0

  • eBook Packages: Springer Book Archive

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