Structure and Semantics of Arrow Diagrams

Yohei Kurata and Max Egenhofer
Conference on Spatial Information Theory (COSIT '05), Ellicottville, NY
D. Mark and A. Cohn (eds.), Lecture Notes in Computer Science, Springer, September 2005 (in press).

Abstract

Arrows are major components in diagrams, where they are typically used to facilitate the communication of dynamic information. An automated interpretation of arrow diagrams would be highly desirable in pen-based interfaces. This paper develops a method for deducing possible interpretations of individual arrow diagrams. Based on a study of the use of arrow diagrams, we classify their semantics into properties, annotations, actions, and conjunctions. Then, we discuss the structural requirements of arrow diagrams for illustrating each class of semantics, as well as the structural conditions for adding optional components. Finally, we investigate all possible structures of simple arrow diagrams for each class and demonstrate that knowledge of the structure of an arrow reduces the ambiguity of possible semantics.

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