Constraint diagrams: visualizing invariants in object-oriented models
Proceedings of the 12th ACM SIGPLAN conference on Object-oriented programming, systems, languages, and applications
Type-syntax and token-syntax in diagrammatic systems
Proceedings of the international conference on Formal Ontology in Information Systems - Volume 2001
Projections in Venn-Euler Diagrams
VL '00 Proceedings of the 2000 IEEE International Symposium on Visual Languages (VL'00)
VENNFS: A Venn-Diagram File Manager
IV '03 Proceedings of the Seventh International Conference on Information Visualization
Journal of Visual Languages and Computing
Using Euler Diagrams in Traditional Library Environments
Electronic Notes in Theoretical Computer Science (ENTCS)
Exploring the notion of ‘clutter' in euler diagrams
Diagrams'06 Proceedings of the 4th international conference on Diagrammatic Representation and Inference
Efficient on-line algorithms for Euler diagram region computation
Computational Geometry: Theory and Applications
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In logic, there are various normal forms for formulae; for example, disjunctive and conjunctive normal form for formulae of propositional logic or prenex normal form for formulae of predicate logic. There are algorithms for `reducing' a given formula to a semantically equivalent formula in normal form. Normal forms are used in a variety of contexts including proofs of completeness, automated theorem proving, logic programming etc. In this paper, we develop a normal form for unitary Euler diagrams with shading. We give an algorithm for reducing a given Euler diagram to a semantically equivalent diagram in normal form and hence a decision procedure for determining whether two Euler diagrams are semantically equivalent. Potential applications of the normal form include clutter reduction and automated theorem proving in systems based on Euler diagrams.