Skip to main content

Negation in Contextual Logic

  • Conference paper
Conceptual Structures at Work (ICCS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3127))

Included in the following conference series:

Abstract

This contribution discusses a formalization of the “negation of a concept”. The notion of “concept” has been successfully formalized in the early eighties and led to the theory of Formal Concept Analysis. Boole (1815-1864) developed a mathematical theory for human thought based on signs and classes. The formalization of the negation of concepts is needed in order to develop a mathematical theory of human thought based on “concept as a basic unit of thought”. Two approaches will be discussed: negation as a partial or as a full operation on concepts.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Birkhoff, G.: Lattices and their applications. Bull. Amer. Math. Soc. 44, 793–800 (1938)

    Article  MathSciNet  Google Scholar 

  2. Birkhoff, G.: What can lattices do for you? In: Abbott, J.C. (ed.) Trends in lattice Theory, Van Nostrand-Reinhold, New York, pp. 1–40 (1970)

    Google Scholar 

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

    Google Scholar 

  4. Burris, S.: The laws of Boole’s thought.(2000), (preprint) http://www.thoralf.uwaterloo.ca/htdocs/MYWORKS/PREPRINTS/aboole.pdf

  5. Eisler, R.: Wörtebuch der Philosophischen Begriffe. Mittler, Berlin (1929).

    Google Scholar 

  6. Ganter, B., Kwuida, L.: Representable weak dicomplementations on finite lattices. Contributions to General Algebra, J. Heyn Klagenfurt 14, 63–72 (2004)

    Google Scholar 

  7. Grätzer, G.: Lattice theory. First concepts and distributive lattices. A Series of Books in Mathematics. W. H. Freeman and Company, New York (1971)

    Google Scholar 

  8. Ganter, B., Wille, R.: Formal Concept Analysis. Mathematical Foundations. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  9. Ganter, B., Wille, R.: Contextual attribute logic. In: Tepfenhart, W., Cyre, W. (eds.) ICCS 1999. LNCS (LNAI), vol. 1640, pp. 337–338. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  10. von Hentig, H.: Magier oder Magister? Über die Einheit der Wissenschaft im Verständigungsprozess. Aufl. Suhrkamp Frankfurt 1 (1974)

    Google Scholar 

  11. 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 

  12. Kwuida, L.: Weakly dicomplemented lattices, Boolean algebras and double p-algebras. Technical Report MATH-AL-05-2003 (2003)

    Google Scholar 

  13. Kwuida, L.: When is a concept algebra Boolean? In: Eklund, P. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  14. Stumme, G.: Boolesche Begriffe. Diplomarbeit. TH Darmstadt (1994)

    Google Scholar 

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

    Google Scholar 

  16. 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 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kwuida, L., Tepavčević, A., Šešelja, B. (2004). Negation in Contextual Logic. In: Wolff, K.E., Pfeiffer, H.D., Delugach, H.S. (eds) Conceptual Structures at Work. ICCS 2004. Lecture Notes in Computer Science(), vol 3127. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27769-9_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-27769-9_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22392-4

  • Online ISBN: 978-3-540-27769-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics