Diagram Semantics and Scheme Algebra: A Framework for the Analysis and Simulation of Diagrammatic Reasoning

Michael May

(1) Diagrams constitutes a basic type in the classification of the different representational forms based on relations of similarity (i.e. iconic signs). According to C. S. Peirce, there are three basic types of iconic signs: pictures, diagrams and metaphors. Peirce asserted that "all necessary reasoning is diagrammatic" and that "necessary reasoning makes its conclusions evident" by a constructive process leading to the observation of a mental model of the object of the reasoning process. Asserting facts about some situation, introducing hypothetical state of affairs, and drawing conclusions, are somehow similar to constructing, manipulating and observing a diagram.

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