Logic Without Syntax
| dc.creator | Hughes, Dominic | |
| dc.date | 2005-04-04 | |
| dc.date.accessioned | 2026-07-07T05:18:47Z | |
| dc.date.available | 2026-07-07T05:18:47Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0504065 | |
| dc.identifier | http://arxiv.org/abs/math/0504065 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74787 | |
| dc.subject | Logic | |
| dc.subject | Category Theory | |
| dc.title | Logic Without Syntax | |
| dc.type | text |