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  1. Weak Disharmony: Some Lessons for Proof-Theoretic Semantics.Bogdan Dicher - 2016 - Review of Symbolic Logic (3):1-20.
    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 (...)
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  • Subatomic Natural Deduction for a Naturalistic First-Order Language with Non-Primitive Identity.Bartosz Więckowski - 2016 - Journal of Logic, Language and Information 25 (2):215-268.
    A first-order language with a defined identity predicate is proposed whose apparatus for atomic predication is sensitive to grammatical categories of natural language. Subatomic natural deduction systems are defined for this naturalistic first-order language. These systems contain subatomic systems which govern the inferential relations which obtain between naturalistic atomic sentences and between their possibly composite components. As a main result it is shown that normal derivations in the defined systems enjoy the subexpression property which subsumes the subformula property with respect (...)
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  • On a Generality Condition in Proof‐Theoretic Semantics.Bogdan Dicher - 2017 - Theoria 83 (4):394-418.
    In the recent literature on proof-theoretic semantics, there is mention of a generality condition on defining rules. According to this condition, the schematic formulation of the defining rules must be maximally general, in the sense that no restrictions should be placed on the contexts of these rules. In particular, context variables must always be present in the schematic rules and they should range over arbitrary collections of formulae. I argue against imposing such a condition, by showing that it has undesirable (...)
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  • Stabilizing Quantum Disjunction.Luca Tranchini - 2018 - Journal of Philosophical Logic 47 (6):1029-1047.
    Since the appearance of Prior’s tonk, inferentialists tried to formulate conditions that a collection of inference rules for a logical constant has to satisfy in order to succeed in conferring an acceptable meaning to it. Dummett proposed a pair of conditions, dubbed ‘harmony’ and ‘stability’ that have been cashed out in terms of the existence of certain transformations on natural deduction derivations called reductions and expansions. A long standing open problem for this proposal is posed by quantum disjunction: although its (...)
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