Computing reading trees for constraint diagrams

Abstract

Constraint diagrams are a visual notation designed to complement the Unified Modeling Language in the development of software systems. They generalize Venn diagrams and Euler circles, and include facilities for quantification and navigation of relations. Their design emphasizes scalability and expressiveness while retaining intuitiveness. Due to subtleties concerned with the ordering of symbols in this visual language, the formalization of constraint diagrams is non-trivial; some constraint diagrams have more than one intuitive reading. A reading algorithm, which associates a unique semantic interpretation to a constraint diagram, with respect to a reading tree, has been developed. A reading tree provides a partial ordering for syntactic elements of the diagram. Reading trees are obtainable from a partially directed graph, called the dependence graph of the diagram. In this paper we describe a tree-construction algorithm, which utilizes graph transformations in order to produce all possible reading trees from a dependence graph. This work will aid the production of tools which will allow an advanced user to choose from a range of semantic interpretations of a diagram.