A Note on Harmony

Journal of Philosophical Logic 41 (3):613-628 (2012)
In the proof-theoretic semantics approach to meaning, harmony , requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony , requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony : imposes the existence of certain transformations of derivations, known as reduction and expansion . We propose a construction of the E-rules (in GE-form) from given I-rules, and prove that the constructed rules satisfy also local intrinsic harmony. The construction is based on a classification of I-rules, and constitute an implementation to Gentzen’s (and Pawitz’) remark, that E-rules can be “read off” I-rules
Keywords Natural-deduction  Proof-theoretic semantics  Introduction-rules  Elimination-rules  Harmony  Local soundness/completeness
Categories (categorize this paper)
DOI 10.1007/s10992-011-9208-0
 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 Nissim Francez, A Note on Harmony
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
H. P. Barendregt (1984). The Lambda Calculus: Its Syntax and Semantics. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..
Arthur Prior (1967). The Runabout Inference Ticket. In Peter Strawson (ed.), Analysis. Oxford University Press 38-9.

View all 11 references / Add more references

Citations of this work BETA

View all 12 citations / Add more citations

Similar books and articles
Stephen Read (2000). Harmony and Autonomy in Classical Logic. Journal of Philosophical Logic 29 (2):123-154.

Monthly downloads

Added to index


Total downloads

78 ( #43,354 of 1,726,249 )

Recent downloads (6 months)

20 ( #41,183 of 1,726,249 )

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.