This short note shows that the scheme of disjunctive reasoning, a or b, not b : a, does not hold neither in proper ortholattices nor in proper de Morgan algebras. In both cases the scheme, once translated into the inequality b' · (a+b) ≤ a, forces the structure to be a boolean algebra.
@article{urn:eudml:doc:41877,
title = {A short note on lattices allowing disjunctive reasoning.},
journal = {Mathware and Soft Computing},
volume = {13},
year = {2006},
pages = {135-137},
zbl = {1119.03064},
mrnumber = {MR2302686},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41877}
}
Trillas, Enric; Renedo, Eloy; Alsina, Claudi. A short note on lattices allowing disjunctive reasoning.. Mathware and Soft Computing, Tome 13 (2006) pp. 135-137. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41877/