Abstract
Recently, a new algebraic structure called pseudo-equality algebra has been defined by Jenei and Kóródi as a generalization of the equality algebra previously introduced by Jenei. As a main result, it was proved that the pseudo-equality algebras are term equivalent with pseudo-BCK meet-semilattices. We found a gap in the proof of this result and we present a counterexample and a correct version of the theorem. The correct version of the corresponding result for equality algebras is also given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Galatos N., Jipsen P., Kowalski T., Ono H.: Residuated Lattices: An Algebraic Glimpse at Substructural Logics. Elsevier, Amsterdam (2007)
Georgescu, G., Iorgulescu, A.: Pseudo-BCK algebras: An extension of BCK-algebras. In: Proceedings of DMTCS’01: Combinatorics, Computability and Logic, Springer, London, pp. 97–114 (2001)
Iorgulescu A.: Classes of pseudo-BCK algebras—Part I. J. Mult.-Valued Logic Soft Comput. 12, 71–130 (2006)
Jenei S.: Equality algebras. Studia Logica 100, 1201–1209 (2012)
Jenei S., Kóródi L.: Pseudo equality algebras. Arch. Math. Logic 52, 469–481 (2013)
Kühr J.: Pseudo-BCK semilattices. Demonstr. Math. 40, 495–516 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ciungu, L.C. On pseudo-equality algebras. Arch. Math. Logic 53, 561–570 (2014). https://doi.org/10.1007/s00153-014-0380-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00153-014-0380-0
Keywords
- Equality algebra
- Pseudo-equality algebra
- Pseudo-BCK algebra
- Meet-semilattice
- Pseudo-product condition
- Pseudo-distributivity condition
- Pseudo-equality distributivity condition