Constraint diagrams: visualizing invariants in object-oriented models
Proceedings of the 12th ACM SIGPLAN conference on Object-oriented programming, systems, languages, and applications
Towards the principled design of software engineering diagrams
Proceedings of the 22nd international conference on Software engineering
DIAGRAMS '02 Proceedings of the Second International Conference on Diagrammatic Representation and Inference
Visualization of Formal Specifications
APSEC '99 Proceedings of the Sixth Asia Pacific Software Engineering Conference
Aligning syntax and semantics in formalisations of visual languages
HCC '01 Proceedings of the IEEE 2001 Symposia on Human Centric Computing Languages and Environments (HCC'01)
A Decidable Constraint Diagram Reasoning System
Journal of Logic and Computation
Towards Overcoming Deficiencies in Constraint Diagrams
VLHCC '07 Proceedings of the IEEE Symposium on Visual Languages and Human-Centric Computing
Automated Theorem Proving in Euler Diagram Systems
Journal of Automated Reasoning
Evaluating and generalizing constraint diagrams
Journal of Visual Languages and Computing
Generating and drawing area-proportional euler and venn diagrams
Generating and drawing area-proportional euler and venn diagrams
Embedding Wellformed Euler Diagrams
IV '08 Proceedings of the 2008 12th International Conference Information Visualisation
The semantics of augmented constraint diagrams
Journal of Visual Languages and Computing
Diagrammatic Formal Specification of a Configuration Control Platform
Electronic Notes in Theoretical Computer Science (ENTCS)
Diagram interpretation and e-learning systems
Diagrams'10 Proceedings of the 6th international conference on Diagrammatic representation and inference
Heterogeneous reaoning in real arithmetics
Diagrams'10 Proceedings of the 6th 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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Diagrams have been used for centuries in the visualization of mathematical concepts and to aid the exploration and formalization of ideas. This is hardly surprising given the intuitive appeal of visual languages. Thus it seems very natural to establish how diagrams can play an integral part of mathematical formalization and reasoning, giving them the same status as the symbolic languages that they are used alongside. Indeed, recently we have seen the emergence of diagrammatic reasoning systems that are defined with sufficient mathematical rigour to allow them to be used as formal tools in their own right. Some of these systems have been designed with particular application areas in mind, such as number theory and real analysis, or formal logics. This paper focuses on the use of diagrammatic logics to formalize mathematical theories with the same level of rigour that is present in their corresponding predicate logic axiomatizations. In particular, extensions to the constraint diagram logic are proposed to make it more suitable for use in mathematics. This extended logic is illustrated via the diagrammatic formalization of some commonly occurring mathematical concepts. Subsequently, we demonstrate its use in the proofs of some simple theorems.