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.
WEAK DISHARMONY: SOME LESSONS FOR PROOF-THEORETIC SEMANTICS
DICHER, BOGDAN AUGUSTIN
2016-01-01
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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