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  1. 1 Logic and Logical Philosophy

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  1. 1 Francez N.

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  1. 1 2018

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Does the Implication Elimination Rule Need a Minor Premise?

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Francez N.
Logic and Logical Philosophy
|
2018
|
vol. 27
|
issue 3
351-373
EN
The paper introduces NJ g , a variant of Gentzen’s NJ natural deduction system, in which the implication elimination rule has no minor premise. The NJ g -systems extends traditional ND-system with a new kind of action in derivations, assumption incorporation, a kind of dual to the assumption discharge action. As a result, the implication (I/E)-rules are invertible and, almost by definition, harmonious and stable, a major condition imposed by proof-theoretic semantics on ND-systems to qualify as meaning-conferring. There is also a proof-term assignment to NJ g -derivations, materialising the Curry-Howard correspondence for this system.
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