Paper Info
Title
Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization
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.
Year
DOI
Venue
2013
10.1007/s11225-012-9370-6
Studia Logica
Keywords
Field
DocType
Proof theory,Natural deduction,Diagrammatic reasoning,Euler diagrams
Discrete mathematics,Normalization (statistics),Diagrammatic reasoning,Algebra,Natural deduction,Proof theory,Algorithm,Euler diagram,Euler's formula,Mathematical proof,Soundness,Mathematics
Journal
Volume
Issue
ISSN
101
1
0039-3215
Citations 
PageRank 
References 
4
0.45
4
Authors
1
Name
Order
Citations
PageRank
Ryo Takemura1859.52