On the Completeness and Expressiveness of Spider Diagram Systems
Diagrams '00 Proceedings of the First International Conference on Theory and Application of Diagrams
Diagrammatic Reasoning Systems
ICCS '08 Proceedings of the 16th international conference on Conceptual Structures: Knowledge Visualization and Reasoning
Measuring and Reducing Clutter in Euler Diagrams
Electronic Notes in Theoretical Computer Science (ENTCS)
A Survey of Reasoning Systems Based on Euler Diagrams
Electronic Notes in Theoretical Computer Science (ENTCS)
Investigating Reasoning with Constraint Diagrams
Electronic Notes in Theoretical Computer Science (ENTCS)
A Diagrammatic Inference System with Euler Circles
Journal of Logic, Language and Information
Syllogisms in Rudimentary Linear Logic, Diagrammatically
Journal of Logic, Language and Information
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SD2 is a system of Venn-type diagrams that can be used to reason diagrammatically about sets, their cardinalities and their relationships. They augment the systems of Venn-Peirce diagrams investigated by Shin to include lower and upper bounds for the cardinalities of the sets represented by regions of diagrams. This paper summarises their syntax and semantics and introduces inference rules for reasoning with the system. We discuss the soundness of the system and develop a proof strategy for completeness simpler than that adopted by Shin. We expect this strategy to extend to other, richer spider diagram systems and to constraint diagrams, the visual notation that has been used in conjunction with object-oriented modelling notations such as the Unified Modelling Language.