A normal form for spider diagrams of order

We develop a reasoning system for an Euler diagram based visual logic, called spider diagrams of order. We define a normal form for spider diagrams of order and provide an algorithm, based on the reasoning system, for producing diagrams in our normal form. Normal forms for visual logics have been shown to assist in proving completeness of associated reasoning systems. We wish to use the reasoning system to allow future direct comparison of spider diagrams of order and linear temporal logic.