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WEAK DISHARMONY: SOME LESSONS FOR PROOF-THEORETIC SEMANTICS

Published online by Cambridge University Press:  08 August 2016

BOGDAN DICHER
BOGDAN DICHER*
Affiliation:
Department of Pedagogy, Psychology, Philosophy, University of Cagliari
*
*DEPARTMENT OF PEDAGOGY, PSYCHOLOGY, PHILOSOPHY UNIVERSITY OF CAGLIARI CAGLIARI, IS MIRRIONIS 1, 09123 SARDEGNA, ITALY E-mail: bdicher@me.com
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Abstract

A logical constant is weakly disharmonious if its elimination rules are weaker than its introduction rules. Substructural weak disharmony is the weak disharmony generated by structural restrictions on the eliminations. I argue that substructural weak disharmony is not a defect of the constants which exhibit it. To the extent that it is problematic, it calls into question the structural properties of the derivability relation. This prompts us to rethink the issue of controlling the structural properties of a logic by means of harmony. I argue that such a control is possible and desirable. Moreover, it is best achieved by global tests of harmony.

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Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 3 , September 2016 , pp. 583 - 602
Copyright
Copyright © Association for Symbolic Logic 2016 

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