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
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.
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