Boundary Logic and Alpha Existential Graphs

Peirce's Alpha Existential Graphs (AEG) is combined with Spencer Brown's Laws of Form to create an algebraic diagrammatic formalism called boundary logic. First, the intuitive properties of configurations of planar nonoverlapping closed curves are viewed as a pure boundary mathematics, without conventional interpretation. Void representational space provides a featureless substrate for boundary forms. Pattern-equations impose constraints on forms to define semantic interpretation. Patterns emphasize void-equivalence, deletion of structure that is syntactically irrelevant and semantically inert. Boundary logic maps one-to-many to propositional calculus. However, the three simple pattern-equations of boundary logic provide capabilities that are unavailable in token-based systems. Void-substitution replaces collection and rearrangement of forms. Patterns incorporate transparent boundaries that ignore the arity and scope of logical connectives. The algebra is isomorphic to AEG but eliminates difficulties with reading and with use by substituting a purely diagrammatic formalism for the logical mechanisms incorporated within AEG.