Constraint diagrams: visualizing invariants in object-oriented models
Proceedings of the 12th ACM SIGPLAN conference on Object-oriented programming, systems, languages, and applications
Logical reasoning with diagrams
Logical reasoning with diagrams
The Unified Modeling Language reference manual
The Unified Modeling Language reference manual
Logic and Visual Information
Constraint Diagrams: A Step Beyond UML
TOOLS '99 Proceedings of the Technology of Object-Oriented Languages and Systems
VL '99 Proceedings of the IEEE Symposium on Visual Languages
Reasoning with Spider Diagrams
VL '99 Proceedings of the IEEE Symposium on Visual Languages
SD2: A Sound and Complete Diagrammatic Reasoning System
VL '00 Proceedings of the 2000 IEEE International Symposium on Visual Languages (VL'00)
Using Animation in Diagrammatic Theorem Proving
DIAGRAMS '02 Proceedings of the Second International Conference on Diagrammatic Representation and Inference
DIAGRAMS '02 Proceedings of the Second International Conference on Diagrammatic Representation and Inference
Corresponding Regions in Euler Diagrams
DIAGRAMS '02 Proceedings of the Second International Conference on Diagrammatic Representation and Inference
Diagrammatic Reasoning Systems
ICCS '08 Proceedings of the 16th international conference on Conceptual Structures: Knowledge Visualization and Reasoning
The Advent of Formal Diagrammatic Reasoning Systems
ICFCA '09 Proceedings of the 7th International Conference on Formal Concept Analysis
Temporal graph queries to support software evolution
ICGT'06 Proceedings of the Third international conference on Graph Transformations
Syllogisms in Rudimentary Linear Logic, Diagrammatically
Journal of Logic, Language and Information
Twelve years of diagrams research
Journal of Visual Languages and Computing
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Spider diagram systems provide a visual language that extends the popular and intuitive Venn diagrams and Euler circles. Designed to complement object-oriented modelling notations in the specification of large software systems they can be used to reason diagrammatically about sets, their cardinalities and their relationships with other sets. A set of reasoning rules for a spider diagram system is shown to be sound and complete. We discuss the extension of this result to diagrammatically richer notations and also consider their expressiveness. Finally, we show that for a rich enough system we can diagrammatically express the negation of any diagram.