Title :
On three laws typical of Booleanity
Author :
Trillas, Enric ; Renedo, Eloy ; Alsina, Claud
Author_Institution :
Dept. de Inteligencia Aritificial, Univ. Politecnica de Madrid, Spain
Abstract :
This paper´s goal is to prove that the only de Morgan algebras and the only ortholattices in which the three laws a´+b = a´+a.b,a.(a´+b)≤b, and (a.b´)´= b + a´b´ do hold, are Boolean algebras. That is, in those two usual generalizations of Boolean algebras these laws characterize Booleanity.
Keywords :
Boolean algebra; fuzzy logic; Boolean algebras; de Morgan algebras; fuzzy logic; ortholattices; Boolean algebra; Equations; Fuzzy logic; Fuzzy set theory; Lattices;
Conference_Titel :
Fuzzy Information, 2004. Processing NAFIPS '04. IEEE Annual Meeting of the
Print_ISBN :
0-7803-8376-1
DOI :
10.1109/NAFIPS.2004.1337354
