Logic Journal of the IGPL 10 (3):299-337 (2002)

Authors
Neil Tennant
Ohio State University
Abstract
The system of natural deduction that originated with Gentzen , and for which Prawitz proved a normalization theorem, is re-cast so that all elimination rules are in parallel form. This enables one to prove a very exigent normalization theorem. The normal forms that it provides have all disjunction-eliminations as low as possible, and have no major premisses for eliminations standing as conclusions of any rules. Normal natural deductions are isomorphic to cut-free, weakening-free sequent proofs. This form of normalization theorem renders unnecessary Gentzen's resort to sequent calculi in order to establish the desired metalogical properties of his logical system.Ultimate normal forms are well-adapted to the needs of the computational logician, affording valuable constraints on proof-search. They also provide an analysis of deductive relevance. There is a deep isomorphism between natural deductions and sequent proofs in the relevantized system
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DOI 10.1093/jigpal/10.3.299
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References found in this work BETA

The Taming of the True.Neil Tennant - 1997 - Oxford University Press.
A Natural Extension of Natural Deduction.Peter Schroeder-Heister - 1984 - Journal of Symbolic Logic 49 (4):1284-1300.
The Undecidability of Entailment and Relevant Implication.Alasdair Urquhart - 1984 - Journal of Symbolic Logic 49 (4):1059-1073.

View all 15 references / Add more references

Citations of this work BETA

Analytic Rules for Mereology.Paolo Maffezioli - 2016 - Studia Logica 104 (1):79-114.
Why Intuitionistic Relevant Logic Cannot Be a Core Logic.Joseph Vidal-Rosset - 2017 - Notre Dame Journal of Formal Logic 58 (2):241-248.

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