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.
| Autores: | , , |
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| 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 |
| 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. |
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