A Note on Harmony

Journal of Philosophical Logic 41 (3):613-628 (2012)
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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.

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Nissim Francez
Technion, Israel Institute of Technology

Citations of this work

General-Elimination Harmony and the Meaning of the Logical Constants.Stephen Read - 2010 - Journal of Philosophical Logic 39 (5):557-576.
.Luca Incurvati & Julian J. Schlöder - 2023 - New York: Oxford University Press USA.
General-Elimination Stability.Bruno Jacinto & Stephen Read - 2017 - Studia Logica 105 (2):361-405.

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