Statecharts: A visual formalism for complex systems
Science of Computer Programming
Communications of the ACM
Constraint diagrams: visualizing invariants in object-oriented models
Proceedings of the 12th ACM SIGPLAN conference on Object-oriented programming, systems, languages, and applications
Logic and Visual Information
Using Animation in Diagrammatic Theorem Proving
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
A Visualization of OCL Using Collaborations
«UML» '01 Proceedings of the 4th International Conference on The Unified Modeling Language, Modeling Languages, Concepts, and Tools
Towards a Formalization of Constraint Diagrams
HCC '01 Proceedings of the IEEE 2001 Symposia on Human Centric Computing Languages and Environments (HCC'01)
The Logic System of Concept Graphs With Negation: And Its Relationship to Predicate Logic
The Logic System of Concept Graphs With Negation: And Its Relationship to Predicate Logic
The Expressiveness of Spider Diagrams
Journal of Logic and Computation
A reading algorithm for constraint diagrams
HCC '03 Proceedings of the 2003 IEEE Symposium on Human Centric Computing Languages and Environments
Investigating Reasoning with Constraint Diagrams
Electronic Notes in Theoretical Computer Science (ENTCS)
Towards Overcoming Deficiencies in Constraint Diagrams
VLHCC '07 Proceedings of the IEEE Symposium on Visual Languages and Human-Centric Computing
Evaluating and generalizing constraint diagrams
Journal of Visual Languages and Computing
A diagrammatic reasoning system for the description logic ALC
Journal of Visual Languages and Computing
Diagrammatic Reasoning Systems
ICCS '08 Proceedings of the 16th international conference on Conceptual Structures: Knowledge Visualization and Reasoning
ICCS '08 Proceedings of the 16th international conference on Conceptual Structures: Knowledge Visualization and Reasoning
Visual Mathematics: Diagrammatic Formalization and Proof
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Journal of Visual Languages and Computing
The expressiveness of spider diagrams augmented with constants
Journal of Visual Languages and Computing
Exploring Human Factors in Formal Diagram Usage
Engineering Interactive Systems
The Advent of Formal Diagrammatic Reasoning Systems
ICFCA '09 Proceedings of the 7th International Conference on Formal Concept Analysis
Diagrammatic Formal Specification of a Configuration Control Platform
Electronic Notes in Theoretical Computer Science (ENTCS)
Abstractions of Euler Diagrams
Electronic Notes in Theoretical Computer Science (ENTCS)
Heterogeneous Reasoning with Euler/Venn Diagrams Containing Named Constants and FOL
Electronic Notes in Theoretical Computer Science (ENTCS)
Investigating Reasoning with Constraint Diagrams
Electronic Notes in Theoretical Computer Science (ENTCS)
Model Transformation From VisualOCL to OCL Using Graph Transformation
Electronic Notes in Theoretical Computer Science (ENTCS)
Efficient on-line algorithms for Euler diagram region computation
Computational Geometry: Theory and Applications
A decision procedure for a decidable fragment of generalized constraint diagrams
Journal of Visual Languages and Computing
Using VCL as an aspect-oriented approach to requirements modelling
Transactions on aspect-oriented software development VII
Using VCL as an aspect-oriented approach to requirements modelling
Transactions on aspect-oriented software development VII
Building VCL models and automatically generating Z specifications from them
FM'11 Proceedings of the 17th international conference on Formal methods
Diagrams'12 Proceedings of the 7th international conference on Diagrammatic Representation and Inference
Visualizing and specifying ontologies using diagrammatic logics
AOW '09 Proceedings of the Fifth Australasian Ontology Workshop - Volume 112
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Constraint diagrams are a diagrammatic notation which may be used to express logical constraints. They generalize Venn diagrams and Euler circles, and include syntax for quantification and navigation of relations. The notation was designed to complement the Unified Modelling Language in the development of software systems. Since symbols representing quantification in a diagrammatic language can be naturally ordered in multiple ways, some constraint diagrams have more than one intuitive meaning in first-order predicate logic. Any equally expressive notation which is based on Euler diagrams and conveys logical statements using explicit quantification will have to address this problem. We explicitly augment constraint diagrams with reading trees, which provides a partial ordering for the quantifiers (determining their scope as well as their relative ordering). Alternative approaches using spatial arrangements of components, or alphabetical ordering of symbols, for example, can be seen as implicit representations of a reading tree. Whether the reading tree accompanies the diagram explicitly (optimizing expressiveness) or implicitly (simplifying diagram syntax), we show how to construct unambiguous semantics for the augmented constraint diagram.