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

Authors
Nissim Francez
Technion, Israel Institute of Technology
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
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DOI 10.1007/s10992-011-9208-0
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References found in this work BETA

The Logical Basis of Metaphysics.Michael Dummett - 1991 - Harvard University Press.
The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38.
The Logical Basis of Metaphysics.Michael Dummett, Hilary Putnam & James Conant - 1994 - Philosophical Quarterly 44 (177):519-527.
The Runabout Inference Ticket.Arthur Prior - 1967 - In Peter Strawson (ed.), Analysis. Oxford University Press. pp. 38-9.

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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.

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