Eight Inference Rules for Implication

Studia Logica:1-28 (forthcoming)
Utilizing an idea that has its first appearance in Gerhard Gentzen’s unpublished manuscripts, we generate an exhaustive repertoire of all the possible inference rules that are related to the left implication inference rule of the sequent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.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/s11225-018-9821-9
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 36,555
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Investigations Into a Left-Structural Right-Substructural Sequent Calculus.Lloyd Humberstone - 2007 - Journal of Logic, Language and Information 16 (2):141-171.
Implication with Possible Exceptions.Herman Jurjus & Harrie de Swart - 2001 - Journal of Symbolic Logic 66 (2):517 - 535.
Implication with Possible Exceptions.Herman Jurjus & Harrie de Swart - 2001 - Journal of Symbolic Logic 66 (2):517-535.
Locality for Classical Logic.Kai Brünnler - 2006 - Notre Dame Journal of Formal Logic 47 (4):557-580.
Conjunction Without Conditions in Illative Combinatory Logic.M. Bunder - 1984 - Bulletin of the Section of Logic 13 (4):207-213.
A Minimal Classical Sequent Calculus Free of Structural Rules.Dominic Hughes - 2010 - Annals of Pure and Applied Logic 161 (10):1244-1253.


Added to PP index

Total downloads
8 ( #609,295 of 2,302,572 )

Recent downloads (6 months)
8 ( #69,145 of 2,302,572 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature