Reasoning with spider diagrams

Abstract

Spider diagrams combine and extend Venn diagrams and Euler circles to express constraints on sets and their relationships with other sets. These diagrams can usefully be used in conjunction with object-oriented modelling notations such as the Unified Modelling Language (UML). This paper summarises the main syntax and semantics of spider diagrams and introduces four inference rules for reasoning with spider diagrams and a rule governing the equivalence of the Venn and Euler forms of spider diagrams. This paper also details rules for combining two spider diagrams to produce a single diagram which retains as much of their combined semantic information as possible, and discusses disjunctive diagrams as one possible way of enriching the system in order to combine spider diagrams so that no semantic information is lost.