Bl-algebras and Quantum Structures

  title={Bl-algebras and Quantum Structures},
  author={Thomas Vetterlein},
Endowing a lower-bounded partially ordered set with a total addition or with a total difference operation leads to the basic notion of a NAM, that is, a naturally ordered abelian monoid, or a BCK-algebra, respectively. BL-algebras may be alteratively viewed as certain NAMs or certain BCK-algebras. We characterize the appropriate subclasses by making use of those properties which have been so far considered in an apparently rather different context, namely for certain quantum structures. The… CONTINUE READING

From This Paper

Topics from this paper.
5 Citations
13 References
Similar Papers


Publications referenced by this paper.
Showing 1-10 of 13 references


  • R. Cignoli
  • M. L. D’Ottaviano, D. Mundici, “Algebraic…
  • 2000
Highly Influential
4 Excerpts

Pseudo BL-algebras and DRl-monoids

  • J. Kühr
  • Math. Bohem
  • 2003

New trends in quantum structures

  • A. Dvurečenskij, S. Pulmannová
  • Kluwer Academic Publ., Dordrecht, and Ister…
  • 2000
1 Excerpt

On representations of commutative BCK-algebras

  • DvGr A. Dvurečenskij, M. G. Graziano
  • Demonstratio Math
  • 1999

On a structure theory of effect algebras, Ph.D

  • K. Ravindran
  • 1996

eds.), “Non-classical logics and their applications to fuzzy subsets. A handbook of the mathematical foundations of fuzzy set theory

  • U. Höhle, Commutative, residuated l-monoids, in U. Höhle
  • Kluwer Acad. Publ., Dordrecht
  • 1995

Effect algebras and unsharp quantum logics

  • D. J. Foulis, M. K. Bennett
  • Found. Phys
  • 1994

Similar Papers

Loading similar papers…