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

• Autorzy: Kulpa Z.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

diagrammatic representation; diagrammatic reasoning; diagrammatic reasoning errors; analogical limits; self-consistency; diagram imprecision; impossible cases; impossible figures

• Wydawca: Institute of Information Technology of the Warsaw University of Life Sciences – SGGW
• Czasopismo: Machine Graphics and Vision
• Rocznik: 2003
• Tom: Vol. 12, No. 1
• Strony: 147--160
• Opis fizyczny: Bibliogr. 15 poz., rys.

Twórcy

autor

Kulpa Z.

• Institute of Fundamental Technological Research, Polish Academy of Sciences, ul. Świętokrzyska 21, 00-049 Warsaw, Poland,

Bibliografia

• [1] Penrose L.S., Penrose R.: lmpossible objects: A special type of visual illusion. Brit. J. Psychol., 49(1), 31-33. 1958.
• [2] Jeleńnski S.: Lilavati (In Polish). PZWS, Warsaw. 1968.
• [3] Arnheim R.: Visual Thinking. University of California Press, Berkeley, CA. 1969.
• [4] Huffman D.A.: Impossible objects as nonsense sentences. B. Meltzer, D. Michie (Eds.): Machine Intelligence, 6, Edinburgh University Press, Edinburgh, 295-323. 1971.
• [5] Raushenbakh B.V.: Spatial Constructions in Visual Art. (In Russian). Nauka, Moscow. 1980.
• [6] Kulpa Z.: Are impossible figures possible? Signal Processing, 5(3), 201-220. 1983.
• [7] Deręgowski J.B.: Distortion in Art: The Eye and the Mind. Routlege & Kegan Paul, London. 1984.
• [8] Kulpa Z.: Putting order in the impossible. Perception, 16, 201-214. 1987.
• [9] Kulpa Z.: Diagrammatic representation and reasoning. MG&V, 3(1-2), 77-103. 1994.
• [10] Barwise J., Etchemendy J.: Visual information and valid reasoning. G. Allwein, J. Barwise (Eds.): Logical Reasoning with Diagrams. Oxford University Press, Oxford, 3-25. 1996.
• [11] Shimojima A.: Operational constraints in diagrammatic reasoning. G. Allwein, J. Barwise (Eds.): Logical Reasoning with Diagrams. Oxford University Press, Oxford, 27-48. 1996.
• [12] Lemon O., Pratt I.: Spatial logic and the complexity of diagrammatic reasoning. MG&V, 6(1), 77-88. 1997.
• [13] Kulpa Z.: Foundations of Diagrammatics. (In Polish) Lecture Notes, BWSBil , Bielsko-Biała, Poland. 2000.
• [14] Lemon O.: Comparing the efficacy of visual languages. D. Barker-Plummer, D. Beaver, J. van Benthem, P. Scotta di Luzio (Eds.): Words, Proofs, and Diagrams. CSLI Publications, Stanford , CA, 47-69. 2002.
• [15] Shin S.-J., Lemon O.: Diagrams. E.N. Zalta (Ed.): The Stanford Encyclopedia of Philosophy (Summer 2002 Edition). URL= < http://plato.stanford.edu/archives/sum2002/entries/diagrams/>. 2002.