The "Laws of Form" as a Categorical Logic for Ortho-Lattices

The Laws of Form as a Categorical Logic
http://federation.g3z.com/Mathematics/index.htm#SpencerBrown

This article, originating from a USENET article from 1994, is an
explication of Spencer Brown's Laws of Form.

The Laws of Form is presented (and generalized) to a categorical logic
whose distinguishing feature is (as in Spencer Brown's original) the
reversibility of the arrows. Such a structure is otherwise known as a
groupoid. The particular categorical structure in question also has
the structure of a Cartesian category.

However, the categorical logic underlying the Spencer Brown system
goes beyond merely a categorification of the proof theory of Boolean
logic. It generalizes to a categorical proof theory for ortholattices;
thus, also to Quantum logic. This serves to complete the analogy
(Curry-Howard:Intuitionistic logic) = (???: "Ortho"-logic).

Hence, the Spencer-Brown system is none other than the extension of
the Curry-Howard isomorphism beyond the realm of Heyting lattices &
Intuitionistic logic to ortho-lattices.

.