Self-consistency, imprecision, and impossible cases in diagrammatic representations
Zenon Kulpa · Machine Graphics & Vision International Journal archive · 2003
The main argument against the use of diagrams in rigorous reasoning is that they are unreliable. Thus, a serious error source analysis 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 general 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.