On Inversion Principles

History and Philosophy of Logic 29 (2):103-113 (2008)
The idea of an ?inversion principle?, and the name itself, originated in the work of Paul Lorenzen in the 1950s, as a method to generate new admissible rules within a certain syntactic context. Some fifteen years later, the idea was taken up by Dag Prawitz to devise a strategy of normalization for natural deduction calculi (this being an analogue of Gentzen's cut-elimination theorem for sequent calculi). Later, Prawitz used the inversion principle again, attributing it with a semantic role. Still working in natural deduction calculi, he formulated a general type of schematic introduction rules to be matched ? thanks to the idea supporting the inversion principle ? by a corresponding general schematic Elimination rule. This was an attempt to provide a solution to the problem suggested by the often quoted note of Gentzen. According to Gentzen ?it should be possible to display the elimination rules as unique functions of the corresponding introduction rules on the basis of certain requirements?. Many people have since worked on this topic, which can be appropriately seen as the birthplace of what are now referred to as ?general elimination rules?, recently studied thoroughly by Sara Negri and Jan von Plato. In this study, we retrace the main threads of this chapter of proof-theoretical investigation, using Lorenzen's original framework as a general guide
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1080/01445340701830334
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 30,370
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
Harmony and Autonomy in Classical Logic.Stephen Read - 2000 - Journal of Philosophical Logic 29 (2):123-154.
A Natural Extension of Natural Deduction.Peter Schroeder-Heister - 1984 - Journal of Symbolic Logic 49 (4):1284-1300.
Ideas and Results in Proof Theory.Dag Prawitz & J. E. Fenstad - 1975 - Journal of Symbolic Logic 40 (2):232-234.

View all 9 references / Add more references

Citations of this work BETA
General-Elimination Harmony and the Meaning of the Logical Constants.Stephen Read - 2010 - Journal of Philosophical Logic 39 (5):557-576.
Harmonising Harmony.Luca Tranchini - 2015 - Review of Symbolic Logic 8 (3):411-423.

Add more citations

Similar books and articles
Added to PP index

Total downloads
47 ( #114,165 of 2,193,782 )

Recent downloads (6 months)
1 ( #290,980 of 2,193,782 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature