Constraint diagrams: visualizing invariants in object-oriented models
Proceedings of the 12th ACM SIGPLAN conference on Object-oriented programming, systems, languages, and applications
Formal languages: an introduction and a synopsis
Handbook of formal languages, vol. 1
Type-syntax and token-syntax in diagrammatic systems
Proceedings of the international conference on Formal Ontology in Information Systems - Volume 2001
VL '99 Proceedings of the IEEE Symposium on Visual Languages
The Expressiveness of Spider Diagrams
Journal of Logic and Computation
General Euler Diagram Generation
Diagrams '08 Proceedings of the 5th international conference on Diagrammatic Representation and Inference
Spider Diagrams of Order and a Hierarchy of Star-Free Regular Languages
Diagrams '08 Proceedings of the 5th international conference on Diagrammatic Representation and Inference
Diagrammatic Reasoning System with Euler Circles: Theory and Experiment Design
Diagrams '08 Proceedings of the 5th international conference on Diagrammatic Representation and Inference
Journal of Computer and System Sciences
Introducing Second-Order Spider Diagrams for Defining Regular Languages
VLHCC '10 Proceedings of the 2010 IEEE Symposium on Visual Languages and Human-Centric Computing
Speedith: a diagrammatic reasoner for spider diagrams
Diagrams'12 Proceedings of the 7th international conference on Diagrammatic Representation and Inference
On the expressiveness of spider diagrams and commutative star-free regular languages
Journal of Visual Languages and Computing
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Existing diagrammatic notations based on Euler diagrams are mostly limited in expressiveness to monadic first-order logic with an order predicate. The most expressive monadic diagrammatic notation is known as spider diagrams of order. A primary contribution of this paper is to develop and formalise a second-order diagrammatic logic, called second-order spider diagrams, extending spider diagrams of order. A motivation for this lies in the limited expressiveness of first-order logics. They are incapable of defining a variety of common properties, like 'is even', which are second-order definable. We show that second-order spider diagrams are at least as expressive as monadic second-order logic. This result is proved by giving a method for constructing a second-order spider diagram for any regular expression. Since monadic second-order logic sentences and regular expressions are equivalent in expressive power, this shows second-order spider diagrams can express any sentence of monadic second-order logic.