The workhorse of Boundary Logic is *Pervasion*, which has no analog in conventional techniques.

A {A B} = A {B}

The curly brace is a *meta-boundary*, standing in place of any spatially intervening content, including none. Curly braces identify *semipermeable boundaries*, a defining characteristic of boundary logic.

Boundary logic proof of the *self-distributive law of the conditional* is illustrated below. The three reduction rules will reduce any TRUE form to a mark. A logical interpretation of *Pervasion* would delete deeply nested connectives and their arguments that match forms anywhere in their context.

(p→(q→r))→((p→q)→(p→r)) theorem ((p)(q) r) ((p) q) (p) r transcribe ( (q) ) ( q) (p) r pervasion ( ) ( q) (p) r pervasion ((( ) ( q) (p) r)) involution ( ) occlusion


Bricken - 2006 - The Mathematics of Boundaries. A Beginning, p. 71–72 (The Map to Logic)

Distributive law in logic. math.stackexchange