%0 Journal Article %1 cheng01 %A Cheng, Peter C. H. %A Cupit, James %A Shadbolt, Nigel R. %D 2001 %J International Journal of Human-Computer Studies %K representation graphs ontology cartesian knowledge diagram acquisition %N 4 %P 457--494 %T Supporting diagrammatic knowledge acquisition: an ontological analysis of Cartesian graphs %U http://www.cs.toronto.edu/~nernst/papers/shadbolt-viz-cartesiangraphs.pdf %V 54 %X Cartesian graphs constitute an important class of previous termknowledgenext term representation devices. As part of a project on diagrammatic previous termknowledgenext term 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 previous termvisualizingnext term 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 previous termknowledgenext term acquisition with Cartesian graphs.

@article{cheng01, abstract = {Cartesian graphs constitute an important class of previous termknowledgenext term representation devices. As part of a project on diagrammatic previous termknowledgenext term 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 previous termvisualizingnext term 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 previous termknowledgenext term acquisition with Cartesian graphs.}, added-at = {2006-09-09T19:24:16.000+0200}, author = {Cheng, Peter C. H. and Cupit, James and Shadbolt, Nigel R.}, biburl = {https://www.bibsonomy.org/bibtex/29b3051db0b8f397957fac29b1c81af7f/neilernst}, citeulike-article-id = {111783}, comment = {Many tools produce graphs; "Despite the potential of such systems the graphs produced are often poorly designed and hinder rather than enhance comprehension (e.g. Tufte, 1983). These tools leave to the user the diffcult task of selecting appropriate forms of graphs and composing them into e!ective representations." "The forms of representation used in knowledge elicitation are typically tied closely to the underlying notational systems used in knowledge-based systems, such as logic and production rules. However, such formalisms may be unfamiliar to domains experts and of a form wholly unlike the representations experts actually use to understand their domains. Using representations for knowledge acquisition that are normally used by the experts may be an e!ective way to overcome the knowledge acquisition bottleneck. Findings in Psychology and Cognitive Science have demonstrated that di!erent representations of the same problem can decrease the diffculty of the problem (Larkin \& Simon, 1987; Cheng \& Simon, 1995), by over an order of magnitude in some cases (Kotovsky, Hayes \& Simon, 1985). It has been shown that diagrammatic representations can sometimes be more effective than the equivalent propositional representations. In the light of these findings it is natural to wonder if using diagrammatic representations might facilitate knowledge acquisition." - some interesting thoughts but a little outside my domain}, description = {sdasda}, interhash = {6669d6d1109fa76dcd494fc17774a966}, intrahash = {9b3051db0b8f397957fac29b1c81af7f}, journal = {International Journal of Human-Computer Studies}, keywords = {representation graphs ontology cartesian knowledge diagram acquisition}, number = 4, pages = {457--494}, pdf = {shadbolt-viz-cartesiangraphs.pdf}, priority = {0}, timestamp = {2006-09-09T19:24:16.000+0200}, title = {Supporting diagrammatic knowledge acquisition: an ontological analysis of {C}artesian graphs}, url = {http://www.cs.toronto.edu/~nernst/papers/shadbolt-viz-cartesiangraphs.pdf}, volume = 54, year = 2001 }