  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.
