Diagrammatic Reasoning System with Euler Circles: Theory and Experiment Design

Authors:
Koji Mineshima;Mitsuhiro Okada;Yuri Sato;Ryo Takemura
Affiliations:
Department of Philosophy, Keio University, Tokyo, Japan 108-8345;Department of Philosophy, Keio University, Tokyo, Japan 108-8345;Department of Philosophy, Keio University, Tokyo, Japan 108-8345;Department of Philosophy, Keio University, Tokyo, Japan 108-8345
Venue:
Diagrams '08 Proceedings of the 5th international conference on Diagrammatic Representation and Inference
Year:
2008

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Abstract

In this paper we are concerned with logical and cognitive aspects of reasoning with Euler circles. We give a proof-theoretical analysis of diagrammatic reasoning with Euler circles involving unification and deletion rules. Diagrammatic syllogisticreasoning is characterized as a particular class of the general diagrammatic proofs. Given this proof-theoretical analysis, we present some conjectures on cognitive aspects of reasoning with Euler diagrams. Then we propose a design of experiment for a cognitive psychological study.