The Mathematics of Diagrammatic Logical Systems

The focus of my PhD was on spider diagrams and constraint diagrams. Constraint diagrams are a visual language for expressing logical statements. The spider diagram language forms a fragment of the constraint diagram language. I developed two diagrammatic reasoning systems. The first of these, based on spider diagrams, directly extends previous work. The second system is based on the more expressive constraint diagram notation and is a restricted form of the language introduced by Kent. I formalized the syntax and semantics of this restricted constraint diagram language, developed reasoning rules and proved soundness and completeness results. I demonstrated that the spider diagram language has the same expressive power as monadic first order logic with equality.