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  1. Faithfulness for naive validity.Ulf Hlobil - 2019 - Synthese 196 (11):4759-4774.
    Nontransitive responses to the validity Curry paradox face a dilemma that was recently formulated by Barrio, Rosenblatt and Tajer. It seems that, in the nontransitive logic ST enriched with a validity predicate, either you cannot prove that all derivable metarules preserve validity, or you can prove that instances of Cut that are not admissible in the logic preserve validity. I respond on behalf of the nontransitive approach. The paper argues, first, that we should reject the detachment principle for naive validity. (...)
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  • Logical Connectives for Constructive Modal Logic.Heinrich Wansing - 2006 - Synthese 150 (3):459-482.
    Model-theoretic proofs of functional completenes along the lines of [McCullough 1971, Journal of Symbolic Logic 36, 15–20] are given for various constructive modal propositional logics with strong negation.
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  • A natural extension of natural deduction.Peter Schroeder-Heister - 1984 - Journal of Symbolic Logic 49 (4):1284-1300.
    The framework of natural deduction is extended by permitting rules as assumptions which may be discharged in the course of a derivation. this leads to the concept of rules of higher levels and to a general schema for introduction and elimination rules for arbitrary n-ary sentential operators. with respect to this schema, (functional) completeness "or", "if..then" and absurdity is proved.
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  • (1 other version)On reduction rules, meaning-as-use, and proof-theoretic semantics.Ruy J. G. B. de Queiroz - 2008 - Studia Logica 90 (2):211-247.
    The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that we suggest an extension (...)
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  • (1 other version)Proof-Theoretic Semantics.Peter Schroeder-Heister - forthcoming - Stanford Encyclopedia of Philosophy.
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  • Proof-Theoretic Functional Completeness for the Hybrid Logics of Everywhere and Elsewhere.Torben Braüner - 2005 - Studia Logica 81 (2):191-226.
    A hybrid logic is obtained by adding to an ordinary modal logic further expressive power in the form of a second sort of propositional symbols called nominals and by adding so-called satisfaction operators. In this paper we consider hybridized versions of S5 (“the logic of everywhere”) and the modal logic of inequality (“the logic of elsewhere”). We give natural deduction systems for the logics and we prove functional completeness results.
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  • (1 other version)On Reduction Rules, Meaning-as-Use, and Proof-Theoretic Semantics.Ruy J. G. B. de Queiroz - 2008 - Studia Logica 90 (2):211 - 247.
    The intention here is that of giving a formal underpinning to the idea of 'meaning-is-use' which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett-Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i. e. the so-called reduction rules. For that we suggest an (...)
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  • On flattening elimination rules.Grigory K. Olkhovikov & Peter Schroeder-Heister - 2014 - Review of Symbolic Logic 7 (1):60-72.
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  • Substructural approaches to paradox: an introduction to the special issue.Elia Zardini - 2021 - Synthese 199 (3):493-525.
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  • Varieties of entailment: introduction to the special issue.Heinrich Wansing & Marco Ruffino - 2020 - Synthese 198 (S22):5207-5211.
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