The semantics of augmented constraint diagrams

Andrew Fish, Jean Flower, John Howse

Research output: Contribution to journalArticlepeer-review


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 al- phabetical ordering of symbols, for example, can be seen as implicit representations of a reading tree. Whether the reading tree accompanies the diagram explicitly (optimizing ex- pressiveness) or implicitly (simplifying diagram syntax), we show how to construct unambiguous semantics for the augmented constraint diagram.
Original languageEnglish
Pages (from-to)541-573
Number of pages33
JournalJournal of Visual Languages and Computing
Issue number6
Publication statusPublished - 1 Dec 2005


  • Visual formalisms
  • Software specification
  • Formal methods
  • Constraint diagrams


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