Skip to main content

Equality Algebras

Abstract

A new structure, called equality algebras, will be introduced. It has two connectives, a meet operation and an equivalence, and a constant. A closure operator will be defined in the class of equality algebras, and we call the closed algebras equivalential. We show that equivalential equality algebras are term equivalent with BCK-algebras with meet. As a by-product, we obtain a quite general result, which is analogous to a result of Kabziński and Wroński: we provide an equational characterization for the equivalential fragment of BCK-algebras with meet.

This is a preview of subscription content, access via your institution.

References

  1. Iogrulescu, A., Algebras of logic as BCK-algebras, Editura ASE, 2008, pp. 569.

  2. Jenei, S., Equality Algebras, Proceedings of the CINTI2010 conference (11th IEEE International Symposium on Computational Intelligence and Informatics), November 18–20, 2010, Budapest, 2010.

  3. Kabziński, J., and A. Wroński, On equivalential algebras, Proceedings of the 1975 International Symposium on Multiple-valued Logic, Indiana University, Bloomington, 1975, pp. 231–243.

  4. Galatos, N., P. Jipsen, T, Kowalski, and H. Ono, Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Studies in Logic and the Foundations of Mathematics Volume 151, 2007, pp. 532.

  5. Iseki K., Tanaka S.: An introduction to the theory of BCK-algebras. Math. Japon. 23, 1–26 (1978)

    Google Scholar 

  6. Novák V., De Baets B.: EQ-algebras. Fuzzy Sets and Systems 160(20), 2956–2978 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sándor Jenei.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Jenei, S. Equality Algebras. Stud Logica 100, 1201–1209 (2012). https://doi.org/10.1007/s11225-012-9457-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-012-9457-0

Keywords

  • BCK-algebra with meet
  • Equivalential fragment
  • Heyting algebra
  • Equivalential algebra
  • Closure operator
  • Term equivalence
  • Equational characterization