A natural extension of natural deduction

Journal of Symbolic Logic 49 (4):1284-1300 (1984)
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Abstract

The framework of natural deduction is extended by permitting rules as assumptions which may be discharged in the course of a derivation. this leads to the concept of rules of higher levels and to a general schema for introduction and elimination rules for arbitrary n-ary sentential operators. with respect to this schema, (functional) completeness "or", "if..then" and absurdity is proved

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References found in this work

Tonk, Plonk and Plink.Nuel Belnap - 1962 - Analysis 22 (6):130-134.
Natural Deduction: A Proof-Theoretical Study.Richmond Thomason - 1965 - Journal of Symbolic Logic 32 (2):255-256.
Natural Logic.H. A. Lewis - 1981 - Philosophical Quarterly 31 (125):376.
The adequacy problem for inferential logic.J. I. Zucker & R. S. Tragesser - 1978 - Journal of Philosophical Logic 7 (1):501 - 516.

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