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JACIII Vol.19 No.6 pp. 861-866
doi: 10.20965/jaciii.2015.p0861
(2015)

Paper:

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An Algebraic Aspect of Correspondences Between Implicational Fragment Logics and Fuzzy Logics

Mayuka F. Kawaguchi* and Michiro Kondo**

*Division of Computer Science and Information Technology, Hokkaido University
Kita 14, Nishi 9, Sapporo 060-0814, Japan

**Tokyo Denki University
2-1200 Muzai Gakuendai, Inzai, Chiba 270-1382, Japan

Received:
May 13, 2015
Accepted:
August 28, 2015
Published:
November 20, 2015
Creative Commons License
Keywords:
implicative algebras, implicational fragment logics, monotone BI-algebras, weakly-associative conjunctive algebras
Abstract
This research report treats a correspondence between implicational fragment logics and fuzzy logics from the viewpoint of their algebraic semantics. The authors introduce monotone BI-algebras by loosening the axiomatic system of BCK-algebras. We also extend the algebras of fuzzy logics with weakly-associative conjunction from the case of the real unit interval to the case of a partially ordered set. As the main result of this report, it is proved that the class of monotone BI-algebras with condition (S) coincides with the class of weakly-associative conjunctive algebras.
Cite this article as:
M. Kawaguchi and M. Kondo, “An Algebraic Aspect of Correspondences Between Implicational Fragment Logics and Fuzzy Logics,” J. Adv. Comput. Intell. Intell. Inform., Vol.19 No.6, pp. 861-866, 2015.
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References
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Last updated on Apr. 22, 2024