Gentzen and Jaśkowski Natural Deduction: Fundamentally Similar but Importantly Different

Gentzen's and Jaśkowski's formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen's formulation more straightforwardly lends itself both to a normalization theorem and to a theory of "meaning" for connectives (which lea...

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Bibliographic Details
Published in:Studia logica 2014-12, Vol.102 (6), p.1103-1142
Main Authors: Hazen, Allen P., Pelletier, Francis Jeffry
Format: Article
Language:English
Subjects:
Computational Linguistics
Education
Free logic
Inference
Intuitionistic logic
Logic
Logical givens
Logical proofs
Mathematical logic
Mathematical Logic and Foundations
Modal logic
Natural deduction calculus
Philosophy
Quantification
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Summary:Gentzen's and Jaśkowski's formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen's formulation more straightforwardly lends itself both to a normalization theorem and to a theory of "meaning" for connectives (which leads to a view of semantics called 'inferentialism'). The present paper investigates cases where Jaskowski's formulation seems better suited. These cases range from the phenomenology and epistemology of proof construction to the ways to incorporate novel logical connectives into the language. We close with a demonstration of this latter aspect by considering a Sheffer function for intuitionistic logic.
ISSN:0039-3215
1572-8730
DOI:10.1007/s11225-014-9564-1