Supporting diagrammatic knowledge acquisition: an ontological analysis of Cartesian graphs

Cartesian graphs constitute an important class of knowledge representation devices. As part of a project on diagrammatic knowledge acquisition we have formulated principles that can underpin the construction, interpretation and use of Cartesian graphs in general and in the specific context of knowledge acquisition. Cartesian graphs are distinguished from other forms of representations by the manner in which they use two-dimensional space to encode quantities on interval or ratio scales. An ontological approach to the analysis of graphs was adopted in which a framework for mapping between the EngMath ontology for engineering mathematics and an ontology of visual components of graphs was developed, the GraphRep framework. GraphRep considers the roles of physical dimensions, measurement units, scales of measurement, functional relations amongst quantities and magnitudes in the generation and interpretation of graphs. It provides a topology of standard graphs and rules for the construction of composite graphs. The utility of the framework is demonstrated by using it: (1) to explain why a particular type of complex composite graph is often used for problem solving in thermodynamics; (2) to analyse the limitations of existing software packages for visualizing data, such as spreadsheets, and to suggest the improvements in their design; and (3) to provide constraints and guidelines for the design of procedures and software to support diagrammatic knowledge acquisition with Cartesian graphs.