, Volume 31, Issue 2, pp 159–187 | Cite as

Unification and Projectivity in De Morgan and Kleene Algebras



We provide a complete classification of solvable instances of the equational unification problem over De Morgan and Kleene algebras with respect to unification type. The key tool is a combinatorial characterization of finitely generated projective De Morgan and Kleene algebras.


Distributive lattices De Morgan and Kleene algebras Unification Projectivity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Adams, M.E.: Principal congruences in De Morgan algebras. Proc. Edinb. Math. Soc. 30, 415–421 (1987)CrossRefMATHGoogle Scholar
  2. 2.
    Baader, F., Snyder, W.: Unification theory. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. 8, pp. 445–533. Elsevier (2001)Google Scholar
  3. 3.
    Balbes, R., Horn, A.: Injective and projective heyting algebras. Trans. Am. Math. Soc. 148, 549–559 (1970)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Balbes, R., Horn, A.: Projective distributive lattices. Pac. J. Math. 33, 273–279 (1970)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Berman, J., Blok, W.J.: Generalizations of Tarski’s fixed point theorem for order varieties of complete meet semilattices. Order 5, 381–392 (1989)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Birkhoff, G.: Rings of sets. Duke Math. J. 3(3), 443–454 (1937)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Cornish, W.H., Fowler, P.R.: Coproducts of De Morgan algebras. Bull. Aust. Math. Soc. 16, 1–13 (1977)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press, Cambridge, UK (2002)CrossRefMATHGoogle Scholar
  9. 9.
    Ghilardi, S.: Unification through projectivity. J. Log. Comput. 7(6), 733–752 (1997)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Kalman, J.A.: Lattices with involution. Trans. Am. Math. Soc. 87, 485–491 (1958)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    MacLane, S.: Categories for the Working Mathematician, 2nd edn. Springer (1998)Google Scholar
  12. 12.
    McKenzie, R., McNulty, G.F., Taylor, W.: Algebras, Lattices, Varieties. Wadsworth and Brooks (1987)Google Scholar
  13. 13.
    Priestley, H.A.: Representation of distributive lattices by means of ordered Stone spaces. Bull. Lond. Math. Soc. 2(2), 186–190 (1970)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Sikorski, R.: Homomorphisms, mappings and retracts. Colloq. Math. 2, 202–211 (1951)MATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institut für InformationssystemeTechnische Universität WienWienAustria
  2. 2.Mathematics InstituteUniversity of BernBernSwitzerland

Personalised recommendations