Propositional logic as Boolean many-valued logic
It is commonly assumed that Boolean logic is synonymous with two-valued logic. However, this needs not be the case. As Boole suspected, and Probability theorists know, one can value propositions in, say, the real unit interval --whatever the purpose of doing this-- and yet preserve the Boolean-algeb...
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| Formato: | informe técnico |
| Fecha de publicación: | 1992 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/370317 |
| Acesso em linha: | https://hdl.handle.net/2117/370317 |
| Access Level: | acceso abierto |
| Palavra-chave: | Algebra, Boolean Àlgebra booleana Àrees temàtiques de la UPC::Informàtica |
| Resumo: | It is commonly assumed that Boolean logic is synonymous with two-valued logic. However, this needs not be the case. As Boole suspected, and Probability theorists know, one can value propositions in, say, the real unit interval --whatever the purpose of doing this-- and yet preserve the Boolean-algebra structure of propositions as well as the common laws of ordinary logic. This report (which is a barely-updated summary of a Ph.D. Thesis written in 1981-82 is an exploration of some of the consequences --some interesting, some a bit unexpected-- of valuing propositions in [0,1]. What emerges is a many-valued logic which is, perhaps surprisingly, also Boolean. All in a neat and natural way. And though the analysis suggests some parallels with Probability Theory, the development falls strictly within the logical theory of Propositional Calculus, to whose classical and well-known version this report aspires to add new insights. Moreover, the expounded theory, initially aimed at a better understanding of logical concepts, turns out to admit a proof theory that has a direct application to hypothetical and approximate reasoning (forced by imprecision or other causes). |
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