A Note on Harmony

Journal of Philosophical Logic 41 (3):613-628 (2012)
Abstract
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
Options
 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
Our Archive
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.
Natural Deduction with General Elimination Rules.Jan von Plato - 2001 - Archive for Mathematical Logic 40 (7):541-567.

View all 10 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.

View all 14 citations / Add more citations

Similar books and articles

Monthly downloads

Added to index

2012-04-27

Total downloads

114 ( #41,726 of 2,153,861 )

Recent downloads (6 months)

10 ( #67,931 of 2,153,861 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums