Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization

Studia Logica 101 (1):157-191 (2013)
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Abstract

Proof-theoretical 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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Citations of this work

World and Logic.Jens Lemanski - 2021 - London, Vereinigtes Königreich: College Publications.
How Diagrams Can Support Syllogistic Reasoning: An Experimental Study.Yuri Sato & Koji Mineshima - 2015 - Journal of Logic, Language and Information 24 (4):409-455.
Speedith: A Reasoner for Spider Diagrams.Matej Urbas, Mateja Jamnik & Gem Stapleton - 2015 - Journal of Logic, Language and Information 24 (4):487-540.

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References found in this work

Ideas and Results in Proof Theory.Dag Prawitz & J. E. Fenstad - 1971 - Journal of Symbolic Logic 40 (2):232-234.
[Omnibus Review].Dag Prawitz - 1991 - Journal of Symbolic Logic 56 (3):1094-1096.

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