Polygonal inequalities as a key to neuronic equations

Neuronic or decision equations, first proposed as a mathematical model of neural activity, have shown, after their exact, compact solution was found, typical behaviours that make them natural tools for General Systems studies. It is shown here that their mathematical investigation is remarkably furthered by generalizing the triangular inequality to polygonal ones. These permit the immediate computation of the tensorial expansion of linearly separable boolean functions, and exhibit clearly the connection between their continuous and discontinuous aspects.