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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.

Diagrammatic spreadsheet

Le T. L., Kulpa Z.

Machine Graphics and Vision

2003

Vol. 12, No. 1

133-146

The diagramatic spreadsheet concept to develop a fully interactive animated diagrammatic system in which the transformation and animation of the diagram is interactively avaible to the user in a click-and-drag mode, and the description of what elements can move, and in what way (according to the required constraints between their components) can be also easily and interactively defined by the user. A constraint is used here like a formula in a spreadsheet, which is employed to automatically recompute the value of a cell whenever any other cells bound to it by the constraint undergo change. The graphical elements of the diagram play the role of spreadsheet cells, and their various attributes constitute the cell contents. The system may be used by human users for interactive exploration of diagrammatic representation and reasoning problems, or as a front-end to a more automatic diagrammatic inference system. In the paper, an overview of this concept and general construction principles of the system are described.

Characterization of convex and pointisable interval relations by diagrammatic methods

Kulpa Z., Le T. L.

Machine Graphics and Vision

2000

Vol. 9, No. 1/2

221-231

In the paper diagrammatic methods are used to demonstrate equivalence of different characterizations of convex and pointisable interval relations. The diagrammatic tools used are introduced: the MR-diagram for interval space, the W-diagram for representing arrangement interval relations, and the conjunction and lattice diagrams. Two theorems on characterizations on convex and pointisable relation classes are given. The proof of the first theorem has been published by Kulpa elsewhere; the second theorem on pointisable relations is proven in this paper with the help of the diagrammatic tools introduced.