Skip to main content
SpringerLink
Log in

Lattice embedding

  • Order-Based Organisation and Encoding
  • Conference paper
  • First Online:
Conceptual Structures: Knowledge Representation as Interlingua (ICCS 1996)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1115))

Included in the following conference series:

  • 219 Accesses

Abstract

In this paper we investigate lattice homomorphism and in particular the embedding problem for lattices which is NP-complete. The use of lattice embedding in knowledge representation is showed by an example.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A.V. Aho, J.E. Hopcroft, and J.D. Ullman. The design and analysis of computer algorithms. Addison-Wesley, 1974.

    Google Scholar 

  2. G. Birkhoff. Lattice theory. American Mathematical Society, 1967.

    Google Scholar 

  3. F. Costello and M.T. Keane. A model-based theory of conceptual combination. In K. Ryan and R. Sutcliffe, editors, AI and Cognitive Science. Springer-Verlag, 1992.

    Google Scholar 

  4. R.P. Dilworth. The role of order in lattice theory. In I. Rival, editor, Ordered sets, pages 333–353. Dordrecht-Boston, 1982.

    Google Scholar 

  5. B.A. Davey and H.A. Priestley. Introduction to lattices and order. Cambridge University Press, 1990.

    Google Scholar 

  6. T. Evans. The word problem for abstract algebras. J. of London Math Soc., 26:64–71, 1951.

    Google Scholar 

  7. J. Farkas. (personal communication), 1994.

    Google Scholar 

  8. M.R. Fellows, J. Kratochvil, M. Middendorf, and F. Pfeiffer. The complexity of induced minors and related problems. Algorithmica, 13(3):266–282, 1995.

    Google Scholar 

  9. S. Foldes. On the complexity of the lattice embeddability problem. Utilitas Mathematica, 17:79–84, 1980.

    Google Scholar 

  10. M.R. Garey and D.S. Johnson. Computers and intractability, A guide to the theory of NP-completeness. W.H. Freeman and co., 1979.

    Google Scholar 

  11. R. Godin and H. Mili. Building and maintaining analysis-level class hierarchies using Galois lattices. ACM SIGPLAN Notices, pages 394–410, 1993.

    Google Scholar 

  12. R. Godin, R. Missaoui, and H. Alaoui. Learning algorithms using a Galois lattice structure. In Ptoc. of the 1991 IEEE Int. Conf. on tools of AI, pages 22–29, San Jose (CA), 1991.

    Google Scholar 

  13. H.P. Grice. Logic and conversation. In P. Cole and J. Morgan, editors, Syntax and semiotics: Speech acts, volume 3, pages 41–58, New York, 1975. Academic Press.

    Google Scholar 

  14. M. Habib. (personal communication), 1996.

    Google Scholar 

  15. M. Habib, M. Morvan, and J.X. Rampon. On the calculation of transitive reduction-closure of orders. Discrete Mathematics, 111:289–303, 1993.

    Google Scholar 

  16. D.S. Johnson. The np-completeness column: An ongoing guide. J. of Algorithms, 3(3):89–99, 1982.

    Google Scholar 

  17. F. Lehmann and R. Wille. A triadic approach to formal concept analysis. In G. Ellis, R. Levinson, W. Rich, and J.F. Sowa, editors, Third Int. Conf. on Conceptual Structures, ICCS'95. Springer-Verlag, 1995.

    Google Scholar 

  18. G. Markowsky. The representation of posets and lattices by sets. Algebra Universalis, 11:173–192, 1980.

    Google Scholar 

  19. R. Missaoui and R.G. Godin. An incremental concept formation approach for learning from databases. In Proc. of the Workshop on Formal Methods of Databases and Software Engineering, pages 39–53, Montreal, 1992.

    Google Scholar 

  20. J.J. Sarbo and J.I. Farkas. Concept sublattices. In Proc. of the European Conference on Machine Learning (ECML'94), Catania, Italy, 1994.

    Google Scholar 

  21. J.J. Sarbo and J.I. Farkas. Knowledge representation and acquisition by concept lattices. In Shaul Markovitch, editor, Proc. of the 11th Izraeli Symposium on Artificial Intelligence (ISAI'95), Hebrew University of Jerusalem, Izrael, 1995.

    Google Scholar 

  22. R. Wille. Aspects of finite lattices. In M. Aigner, editor, Higher combinatorics, pages 79–100. Reidel Publ. Company, 1977.

    Google Scholar 

  23. R. Wille. Restructuring lattice theory: an approach based on hierarchies of concepts. In I. Rival, editor, Ordered sets, pages 445–470. D. Reidel, Dordrecht-Boston, 1982.

    Google Scholar 

  24. R. Wille. Knowledge acquisition by methods of formal concept analysis. In E. Diday, editor, Proc. of the Conf. on Data Analysis, Learning Symbolic and Numeric Knowledge, pages 365–380. Nova Science Publishers, Inc., 1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Nijmegen, Toernooiveld 1, 6525, ED Nijmegen, The Netherlands

    Janos J. Sarbo

Authors
  1. Janos J. Sarbo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Peter W. Eklund Gerard Ellis Graham Mann

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sarbo, J.J. (1996). Lattice embedding. In: Eklund, P.W., Ellis, G., Mann, G. (eds) Conceptual Structures: Knowledge Representation as Interlingua. ICCS 1996. Lecture Notes in Computer Science, vol 1115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61534-2_19

Download citation

  • DOI: https://doi.org/10.1007/3-540-61534-2_19

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61534-7

  • Online ISBN: 978-3-540-68730-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation