In a Boolean Algebra B, an inequality f(x,x --> y)) ≤ y satisfying the condition f(1,1)=1, is considered for defining operations a --> b among the elements of B. These operations are called Conditionals'' for f. In this paper, we obtain all the boolean Conditionals and Internal Conditionals, and some of their properties as, for example, monotonicity are briefly discussed.
@article{urn:eudml:doc:39064,
title = {Modus ponens on Boolean algebras revisited.},
journal = {Mathware and Soft Computing},
volume = {3},
year = {1996},
pages = {105-112},
zbl = {0862.03037},
mrnumber = {MR1414258},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39064}
}
Trillas, Enric; Cubillo, Susana. Modus ponens on Boolean algebras revisited.. Mathware and Soft Computing, Tome 3 (1996) pp. 105-112. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39064/