A short note on lattices allowing disjunctive reasoning

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.

Detalhes bibliográficos
Autores: Trillas i Gay, Enric, Renedo, Eloy, Alsina Català, Claudi|||0000-0002-4430-2241
Tipo de documento: artigo
Data de publicação:2006
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositório:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglês
OAI Identifier:oai:upcommons.upc.edu:2099/3669
Acesso em linha:https://hdl.handle.net/2099/3669
Access Level:Acceso aberto
Palavra-chave:Disjunctive reasoning
Ortholattices
De Morgan algebras
Boolean algebras
Lògica algebraica
Classificació AMS::03 Mathematical logic and foundations::03G Algebraic logic
Descrição
Resumo: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.