Resource data
Logic Without Syntax
Hughes, Dominic
Location:
http://arxiv.org/abs/math/0504065
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.
Belongs to: arXiv
Descargar SCORM
¡Sea el primero en solicitar este recurso!
Para poder solicitar este recurso debe identificarse como usuario de la biblioteca
Users rating
No hay ninguna valoración para este recurso. Sea el primero en
valorar este recurso.
Detalles del recurso
|
Logic Without Syntax
|
| Id. |
20846894 |
| Titulo |
Logic Without Syntax |
| Autor(es) |
Hughes, Dominic |
| Location |
http://arxiv.org/abs/math/0504065
|
| Versión |
1.0 |
| Estado |
Final
|
| 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. |
| Palabras clave |
Mathematics - Logic |
| Tipo de recurso |
Texto Narrativo
|
| Tipo de Interactividad |
Expositivo
|
| Nivel de Interactividad |
muy bajo
|
| Audiencia |
Estudiante
Profesor
Autor
|
| Estructura |
Atomic |
| Coste |
no
|
| Copyright |
sí
|
| Requerimientos técnicos |
Browser: Any |
| Fecha de contribución |
27-mar-2007 |
| Contacto |
|
|