Transitivity of implicative aBE algebras

Denis Zelent

Abstract


We prove that every implicative aBE algebra satisfies the transitivity property. This means that every implicative aBE algebra is a Tarski algebra, and thus is also a commutative BCK algebra.

Keywords


BE algebra; BCK algebra; Tarski algebra; implicativity; transitivity

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References


Imai, Y., Iseki, K., On Axiom Systems of Propositional Calculi. XIV, Proc. Japan Acad. 42 (1966), 19–22. https://doi.org/10.3792/pja/1195522169.

Iorgulescu, A., New generalizations of BCI, BCK and Hilbert algebras – Part I, J. Mult.-Valued Logic Soft Comput. 27 (2016), 353–406.

Iseki, K., Tanaka, S., An introduction to the theory of BCK-algebras, Math. Japon. 23 (1) (1978/79), 1–26.

Jun, Y. B., Kang, M. S., Fuzzifications of generalized Tarski filters in Tarski algebras, Comp. Math. Appl. 61 (2011), 1–7.

Kim, H. S., Kim, Y. H., On BE-algebras, Sci. Math. Jpn. 66 (2007), 113–128

Walendziak, A., The implicative property for some generalizations of BCK algebras, J. Mult.-Valued Logic Soft Comput. 31 (2018), 591–611.

Walendziak, A., On implicative BE algebras, Ann. Univ. Mariae Curie-Skłodowska Sect. A 76 (2) (2022), 45–54.




DOI: http://dx.doi.org/10.17951/a.2022.76.2.55-58
Date of publication: 2023-03-13 22:27:58
Date of submission: 2023-03-12 19:27:32


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