Order

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

Unification and Projectivity in De Morgan and Kleene Algebras

Article

Abstract

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.

Keywords

Distributive lattices De Morgan and Kleene algebras Unification Projectivity 

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References

  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

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