Revistes Catalanes amb Accés Obert (RACO)

A short note on lattices allowing disjunctive reasoning

Enric Trillas i Gay, Eloy Renedo, Claudi Alsina i Català


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.

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