When implication algebras can be residuated lattices?When implication algebras can be residuated lattices?B. Samir, H. Merdach

被引：0

作者：

Basim Samir ^{[1
]}

Huda Merdach ^{[2
]}

机构：

[1] Assiut University,Department of Mathematics, Faculty of Science

[2] Damietta University,Department of Mathematics, Faculty of Science

来源：

Afrika Matematika | 2025年 / 36卷 / 1期

关键词：

Residuated lattice; Implication algebra; DN – residuated lattice; 03G10; 06C15; 03G25;

D O I：

10.1007/s13370-024-01221-5

中图分类号：

学科分类号：

摘要：

M. Ward and R.P. Dilworth were the first to describe the commutative residuated lattices as a generalization of ideal ring lattices. Complete studies on residuated lattices were developed by H. Ono, T. Kowalski, P. Jipsen and C. Tsinakis. Furthermore, Y. Xu is credited with the invention of lattice implication algebra. The aim of the paper was to link up the structures used in foundations of quantum logic and arising in many-valued reasoning. It is shown that implication algebra with unity can be described as residuated lattice.

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