Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization
 Ryo Takemura
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Abstract
Prooftheoretical notions and techniques, developed on the basis of sentential/symbolic representations of formal proofs, are applied to Euler diagrams. A translation of an Euler diagrammatic system into a natural deduction system is given, and the soundness and faithfulness of the translation are proved. Some consequences of the translation are discussed in view of the notion of free ride, which is mainly discussed in the literature of cognitive science as an account of inferential efficacy of diagrams. The translation enables us to formalize and analyze free ride in terms of proof theory. The notion of normal form of Euler diagrammatic proofs is investigated, and a normalization theorem is proved. Some consequences of the theorem are further discussed: in particular, an analysis of the structure of normal diagrammatic proofs; a diagrammatic counterpart of the usual subformula property; and a characterization of diagrammatic proofs compared with natural deduction proofs.
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 Title
 Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization
 Journal

Studia Logica
Volume 101, Issue 1 , pp 157191
 Cover Date
 20130201
 DOI
 10.1007/s1122501293706
 Print ISSN
 00393215
 Online ISSN
 15728730
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Proof theory
 Natural deduction
 Diagrammatic reasoning
 Euler diagrams
 Authors

 Ryo Takemura ^{(1)}
 Author Affiliations

 1. College of Commerce, Nihon University, 521 Kinuta, Setagayaku, Tokyo, 1578570, Japan