The semantics of augmented constraint diagrams

Fish, Andrew, Flower, Jean and Howse, John (2005) The semantics of augmented constraint diagrams Journal of Visual Languages and Computing, 16 (6). pp. 541-573. ISSN 1045-926X

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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 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.

Item Type: Journal article
Uncontrolled Keywords: Visual formalisms; Software specification; Formal methods; Constraint diagrams
Subjects: G000 Computing and Mathematical Sciences > G100 Mathematics
DOI (a stable link to the resource): 10.1016/j.jvlc.2005.03.001
Faculties: Faculty of Science and Engineering > School of Computing, Engineering and Mathematics > Visual Modelling
Depositing User: Converis
Date Deposited: 13 Nov 2007
Last Modified: 14 Apr 2015 13:17

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