A short note on lattices allowing disjunctive reasoning
Eloy Renedo, Claudi Alsina Català · 2006
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.