Diagrammatic reasoning systems

Euler diagrams have been used for centuries as a means for conveying logical statements in a simple, intuitive way. They form the basis of many diagrammatic notations used to represent set-theoretic relationships in a wide range of contexts including software modelling, logical reasoning systems, statistical data representation, database search queries and file system management. In this paper we consider some notations based on Euler diagrams, in particular Spider Diagrams and Constraint Diagrams, with particular emphasis on the development of reasoning systems.