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  1.  10
    Incompleteness of Intuitionistic Propositional Logic with Respect to Proof-Theoretic Semantics.Thomas Piecha & Peter Schroeder-Heister - forthcoming - Studia Logica:1-14.
    Prawitz proposed certain notions of proof-theoretic validity and conjectured that intuitionistic logic is complete for them [11, 12]. Considering propositional logic, we present a general framework of five abstract conditions which any proof-theoretic semantics should obey. Then we formulate several more specific conditions under which the intuitionistic propositional calculus turns out to be semantically incomplete. Here a crucial role is played by the generalized disjunction principle. Turning to concrete semantics, we show that prominent proposals, including Prawitz’s, satisfy at least one (...)
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  2.  30
    Failure of Completeness in Proof-Theoretic Semantics.Thomas Piecha, Wagner de Campos Sanz & Peter Schroeder-Heister - 2015 - Journal of Philosophical Logic 44 (3):321-335.
    Several proof-theoretic notions of validity have been proposed in the literature, for which completeness of intuitionistic logic has been conjectured. We define validity for intuitionistic propositional logic in a way which is common to many of these notions, emphasizing that an appropriate notion of validity must be closed under substitution. In this definition we consider atomic systems whose rules are not only production rules, but may include rules that allow one to discharge assumptions. Our central result shows that Harrop’s rule (...)
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  3.  15
    General Proof Theory: Introduction.Thomas Piecha & Peter Schroeder-Heister - forthcoming - Studia Logica:1-5.
    This special issue on general proof theory collects papers resulting from the conference on general proof theory held in November 2015 in Tübingen.
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  4.  14
    Popper's Notion of Duality and His Theory of Negations.David Binder & Thomas Piecha - 2017 - History and Philosophy of Logic 38 (2):154-189.
    Karl Popper developed a theory of deductive logic in the late 1940s. In his approach, logic is a metalinguistic theory of deducibility relations that are based on certain purely structural rules. Logical constants are then characterized in terms of deducibility relations. Characterizations of this kind are also called inferential definitions by Popper. In this paper, we expound his theory and elaborate some of his ideas and results that in some cases were only sketched by him. Our focus is on Popper's (...)
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  5.  30
    Inversion by Definitional Reflection and the Admissibility of Logical Rules.Wagner de Campos Sanz & Thomas Piecha - 2009 - Review of Symbolic Logic 2 (3):550-569.
    The inversion principle for logical rules expresses a relationship between introduction and elimination rules for logical constants. Hallnäs & Schroeder-Heister (1990, 1991) proposed the principle of definitional reflection, which embodies basic ideas of inversion in the more general context of clausal definitions. For the context of admissibility statements, this has been further elaborated by Schroeder-Heister (2007). Using the framework of definitional reflection and its admissibility interpretation, we show that, in the sequent calculus of minimal propositional logic, the left introduction rules (...)
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  6.  22
    Inversion by Definitional Reflection and the Admissibility of Logical Rules.Wagner Campos Sanz & Thomas Piecha - 2009 - Review of Symbolic Logic 2 (3):550-569.
    The inversion principle for logical rules expresses a relationship between introduction and elimination rules for logical constants. Hallnäs & Schroeder-Heister proposed the principle of definitional reflection, which embodies basic ideas of inversion in the more general context of clausal definitions. For the context of admissibility statements, this has been further elaborated by Schroeder-Heister . Using the framework of definitional reflection and its admissibility interpretation, we show that, in the sequent calculus of minimal propositional logic, the left introduction rules are admissible (...)
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  7. Dialogical Logic.Thomas Piecha - 2015
    Dialogical Logic Dialogical logic is an approach to logic in which the meaning of the logical constants and the notion of validity are explained in game-theoretic terms. The meaning of logical constants like “and”, “or”, “implies”, “not”, “every”, and so forth, is given in terms of how assertions containing these logical constants can … Continue reading Dialogical Logic →.
     
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  8.  2
    A Critical Remark on the BHK Interpretation of Implication.Wagner de Campos Sanz & Thomas Piecha - 2014 - Philosophia Scientae 18:13-22.
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  9. Beyond Logic. Proceedings of the Conference Held in Cerisy-la-Salle, 22-27 May 2017.Thomas Piecha & Jean Fichot (eds.) - 2017
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