Implicative Almost Distributive Lattice

Berhanu Assaye Alaba, Mihret Alamneh, tilahun mekonnen munie


In this paper, we introduce the concept of Implicative Almost Distributive Lattices (IADLs) as a generalization of implicative algebra in the class of Almost Distributive Lattices. We discuss some properties of IADL and derive some equivalent conditions in IADLs. We also discuss some characterizations of IADL to become an implicative algebra.


Almost Distributive Lattice; Implicative Algebras; Implicative Almost Distributive lattice

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X. Yang, “Lattice implication algebras [j],” Journal of Southwest Jiaotong University, vol. 1, 1993.

Y. Xu and K. Qin, “implication algebras and lattice implication algebra classes, j,” Hebei Mining and Civil Engineering Institute, vol. 3, pp. 139–143, 1992.

X. Yang, L. Jun, S. Zhenming, and Q. Keyun, “On semantics of l-valued first-order logic lvft,” International Journal of General System, vol. 29, no. 1, pp. 53–79, 2000.

V. Kolluru and B. Bekele, “Implicative algebras,” Momona Ethiopian Journal of Science, vol. 4, no. 1, pp. 90–101, 2012.

U. Swamy and G. Rao, “Almost distributive lattices,” Journal of the Australian Mathematical Society, vol. 31, no. 1, pp. 77–91, 1981.



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