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Self-consistency, imprecision, and impossible cases in diagrammatic representations

Kulpa Z.

Machine Graphics and Vision

2003

Vol. 12, No. 1

147-160

The main argument against the use of diagrams in rigorous reasoning is that they are unreliable. Thus, a serious error source anlysis for this kind of reasoning should be undertaken, and proper diagrammatic reasoning procedures formulated as a result. As yet, little has been done in this matter. In this paper, one aspect of this problem is addressed, namely errors resulting in generation of so-called impossible cases in diagrammatic representations, violating the property of self-consistency claimed to hold for them. It is shown that the lack of self-consistency is in generar due to limited analogicity of many diagrammatic representations, either because of limited precision of diagrams, or of certain structural properties of the visual language used. Several examples of these effects are shown and analyzed informally, with suggestions for possible remedies and for more formal analysis of the effects.