Quantum Logic in Intuitionistic Perspective
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Quantum Logic in Intuitionistic Perspective
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| Id. |
392631 |
| Titulo |
Quantum Logic in Intuitionistic Perspective |
| Autor(es) |
Coecke, Bob
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| Localización |
http://arxiv.org/abs/math/0011208
Studia Logica 70, 411-440 (2002)
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| Versión |
1.0 |
| Estado |
Final
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| Descripción |
In their seminal paper Birkhoff and von Neumann revealed the following
dilemma: "... whereas for logicians the orthocomplementation properties of
negation were the ones least able to withstand a critical analysis, the study
of mechanics points to the distributive identities as the weakest link in the
algebra of logic." In this paper we eliminate this dilemma, providing a way for
maintaining both. Via the introduction of the "missing" disjunctions in the
lattice of properties of a physical system while inheriting the meet as a
conjunction we obtain a complete Heyting algebra of propositions on physical
properties. In particular there is a bijective correspondence between property
lattices and propositional lattices equipped with a so called operational
resolution, an operation that exposes the properties on the level of the
propositions. If the property lattice goes equipped with an
orthocomplementation, then this bijective correspondence can be refined to one
with propositional lattices equipped with an operational complementation, as
such establishing the claim made above. Formally one rediscovers via physical
and logical considerations as such respectively a specification and a
refinement of the purely mathematical result by Bruns and Lakser (1970) on
injective hulls of meet-semilattices. From our representation we can derive a
truly intuitionistic functional implication on property lattices, as such
confronting claims made in previous writings on the matter. We also make a
detailed analysis of disjunctivity vs. distributivity and finitary vs.
infinitary conjunctivity, we briefly review the Bruns-Lakser construction and
indicate some questions which are left open.
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| Palabras clave |
Mathematics - Logic
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| Tipo de recurso |
Texto Narrativo
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| Tipo de Interactividad |
Expositivo
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| Nivel de Interactividad |
muy bajo
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| Audiencia |
Estudiante
Profesor
Autor
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| Estructura |
Atomic |
| Coste |
no
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| Copyright |
sí
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| Requerimientos técnicos |
Browser: Any
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| Fecha de contribución |
25-feb-2007 |
| Contacto |
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