Eight Inference Rules for Implication

Studia Logica 107 (4):781-808 (2019)
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Abstract

Utilizing an idea that has its first appearance in Gerhard Gentzen’s unpublished manuscripts, we generate an exhaustive repertoire of all the possible inference rules that are related to the left implication inference rule of the sequent calculus from a ground sequent, that is, a logical axiom. We discuss the similarities and differences of these derived rules as well as their interaction with the implication right rule under cut and the structural axiom. We further consider the question of analyticity of cuts in calculi using one of the new rules instead of the standard left implication rule.

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Citations of this work

Comments on the Contributions.Peter Schroeder-Heister - 2024 - In Thomas Piecha & Kai F. Wehmeier (eds.), Peter Schroeder-Heister on Proof-Theoretic Semantics. Springer. pp. 443-455.
The Explosion Calculus.Michael Arndt - 2020 - Studia Logica 108 (3):509-547.
Eight Rules for Implication Elimination.Michael Arndt - 2024 - In Thomas Piecha & Kai F. Wehmeier (eds.), Peter Schroeder-Heister on Proof-Theoretic Semantics. Springer. pp. 239-273.

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References found in this work

Gentzen's proof systems: byproducts in a work of genius.Jan von Plato - 2012 - Bulletin of Symbolic Logic 18 (3):313-367.
Analytic cut.Raymond M. Smullyan - 1968 - Journal of Symbolic Logic 33 (4):560-564.

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