Logic Without Syntax
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Logic Without Syntax
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| Id. |
20846894 |
| Titulo |
Logic Without Syntax |
| Autor(es) |
Hughes, Dominic
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| Localización |
http://arxiv.org/abs/math/0504065
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| Versión |
1.0 |
| Estado |
Final
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| Descripción |
This paper presents an abstract, mathematical formulation of classical
propositional logic. It proceeds layer by layer: (1) abstract, syntax-free
propositions; (2) abstract, syntax-free contraction-weakening proofs; (3)
distribution; (4) axioms (p OR NOT p).
Abstract propositions correspond to objects of the category G(Rel^L) where G
is the Hyland-Tan double glueing construction, Rel is the standard category of
sets and relations, and L is a set of literals.
Abstract proofs are morphisms of a tight orthogonality subcategory of
Gl(Rel^L), where we define Gl as a lax variant of G. We prove that the free
binary product-sum category (contraction-weakening logic) over L is a full
subcategory of Gl(Rel^L), and the free distributive lattice category
(contraction-weakening-distribution logic) is a full subcategory of Gl(Rel^L).
We explore general constructions for adding axioms, which are not Rel-specific
or (p OR NOT p)-specific.
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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 |
27-mar-2007 |
| Contacto |
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