Generalized definitional reflection and the inversion principle

Logica Universalis 1 (2):355-376 (2007)
.  The term inversion principle goes back to Lorenzen who coined it in the early 1950s. It was later used by Prawitz and others to describe the symmetric relationship between introduction and elimination inferences in natural deduction, sometimes also called harmony. In dealing with the invertibility of rules of an arbitrary atomic production system, Lorenzen’s inversion principle has a much wider range than Prawitz’s adaptation to natural deduction. It is closely related to definitional reflection, which is a principle for reasoning on the basis of rule-based atomic definitions, proposed by Hallnäs and Schroeder-Heister. After presenting definitional reflection and the inversion principle, it is shown that the inversion principle can be formally derived from definitional reflection, when the latter is viewed as a principle to establish admissibility. Furthermore, the relationship between definitional reflection and the inversion principle is investigated on the background of a universalization principle, called the ω-principle, which allows one to pass from the set of all defined substitution instances of a sequent to the sequent itself.
Keywords Proof theory  proof-theoretic semantics  definitional reflection  inversion principle  admissibility  inductive definition  logic programming  operative logic  Lorenzen
Categories (categorize this paper)
DOI 10.1007/s11787-007-0018-7
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 15,914
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
Enrico Moriconi & Laura Tesconi (2008). On Inversion Principles. History and Philosophy of Logic 29 (2):103-113.
Luca Tranchini (2015). Harmonising Harmony. Review of Symbolic Logic 8 (3):411-423.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

22 ( #130,611 of 1,725,622 )

Recent downloads (6 months)

6 ( #110,407 of 1,725,622 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.