Graduate studies at Western
Studia Logica 101 (1):157-191 (2013)
|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|
|Keywords||Proof theory Natural deduction Diagrammatic reasoning Euler diagrams|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Koji Mineshima, Mitsuhiro Okada & Ryo Takemura (2012). A Diagrammatic Inference System with Euler Circles. Journal of Logic, Language and Information 21 (3):365-391.
Mateja Jamnik, Alan Bundy & Ian Green (1999). On Automating Diagrammatic Proofs of Arithmetic Arguments. Journal of Logic, Language and Information 8 (3):297-321.
Eric Hammer & Sun-Joo Shin (1998). Euler's Visual Logic. History and Philosophy of Logic 19 (1):1-29.
Nathaniel Miller (2006). A Brief Proof of the Full Completeness of Shin's Venn Diagram Proof System. Journal of Philosophical Logic 35 (3):289 - 291.
Sun-Joo Shin (2012). The Forgotten Individual: Diagrammatic Reasoning in Mathematics. Synthese 186 (1):149-168.
Brice Halimi (2012). Diagrams as Sketches. Synthese 186 (1):387-409.
Keith Stenning & Oliver Lemon (1999). Aligning Logical and Psychological Perspectives on Diagrammatic Reasoning. .
Corin Gurr, John Lee & Keith Stenning (1998). Theories of Diagrammatic Reasoning: Distinguishing Component Problems. [REVIEW] Minds and Machines 8 (4):533-557.
Koji Nakazawa & Makoto Tatsuta (2003). Strong Normalization Proof with CPS-Translation for Second Order Classical Natural Deduction. Journal of Symbolic Logic 68 (3):851-859.
Koji Nakazawa & Makoto Tatsuta (2003). Corrigendum to "Strong Normalization Proof with CPS-Translation for Second Order Classical Natural Deduction". Journal of Symbolic Logic 68 (4):1415-1416.
Solomon Feferman (2012). And so On...: Reasoning with Infinite Diagrams. Synthese 186 (1):371 - 386.
Annalisa Coliva (2012). Human Diagrammatic Reasoning and Seeing-As. Synthese 186 (1):121-148.
Zenon Kulpa (2009). Main Problems of Diagrammatic Reasoning. Part I: The Generalization Problem. [REVIEW] Foundations of Science 14 (1-2):75-96.
Kosta Došen (2003). Identity of Proofs Based on Normalization and Generality. Bulletin of Symbolic Logic 9 (4):477-503.
Atsushi Shimojima & Yasuhiro Katagiri (2013). An Eye-Tracking Study of Exploitations of Spatial Constraints in Diagrammatic Reasoning. Cognitive Science 37 (2):211-254.
Added to index2012-07-19
Total downloads11 ( #107,531 of 739,535 )
Recent downloads (6 months)1 ( #61,778 of 739,535 )
How can I increase my downloads?