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Utilizing an idea that has its first appearance in Gerhard Gentzen’s unpublished manuscripts, we generate an exhaustive repertoire of all the possible inference rules that are related to the left implication inference rule of the sequent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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Supported by the DFG project “Paul Hertz and his foundations of structural proof theory” (DFG AR 1010/2-1).
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Presented by Heinrich Wansing
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Arndt, M. Eight Inference Rules for Implication. Stud Logica 107, 781–808 (2019). https://doi.org/10.1007/s11225-018-9821-9
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DOI: https://doi.org/10.1007/s11225-018-9821-9