Spider Diagrams: A Diagrammatic Reasoning System

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 be used in conjunction with object-oriented modelling notations such as the Unified Modeling Language. This paper summarises the main syntax and semantics of spider diagrams. It also introduces inference rules for reasoning with spider diagrams and a rule for combining spider diagrams. This system is shown to be sound but not complete. Disjunctive diagrams are considered as one way of enriching the system to allow combination of diagrams so that no semantic information is lost. The relationship of this system of spider diagrams to other similar systems, which are known to be sound and complete, is explored briefly.

Heterogeneous Proofs: Spider Diagrams Meet Higher-Order Provers

“…Eventually, with advent of proof theory, their role became almost exclusively that of a visual help. Still, the intuitive nature of diagrams motivated the design of formal diagrammatic reasoning systems -for example, spider diagrams [6] and constraint diagrams [3]. Consequently, some purely diagrammatic theorem provers have been developed, Diamond [8], Edith [10] and Dr.Doodle [13] are some examples.…”

The Advent of Formal Diagrammatic Reasoning Systems

“…They can be thought of as extending Venn-II diagrams. Various different systems exist today, for example [35,36,38,40,74]. In Fig.8, two examples of so-called unary SDs are depicted.…”

Euler Graph Transformations for Euler Diagram Layout

“…They have also formed the basis of a number of visual languages, including spider diagrams [6], Euler/Venn diagrams [14] and Venn-II diagrams [11]. They generalize Venn diagrams [10] because, although they can contain all possible zones (like Venn diagrams), they do not have to.…”