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Proof-Theoretic Semantics: An Autobiographical Survey

In Thomas Piecha & Kai F. Wehmeier (eds.), Peter Schroeder-Heister on Proof-Theoretic Semantics. Springer. pp. 1-51 (2024)

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  1. Ableitbarkeit und Abfolge in der Wissenschaftstheorie Bolzanos.Günter Buhl - 1961 - Köln: Kölner Universitäts-Verlag.
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  • 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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  • (1 other version)Enzyklopädie Philosophie und Wissenschaftstheorie.Jürgen Mittelstraß - 1998 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 29 (2):356-359.
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  • (1 other version)Einführung in die operative Logik und Mathematik.Paul Lorenzen - 1955 - Berlin,: Springer.
    in die operative Logik und Mathematik Zweite Auflage Springer-Verlag Berlin Heidelberg New York 1969 Paul Lorenzen o. Prof. der Philosophie an der Universitat Erlangen Geschaftsfilhrende Herausgeber: Prof. Dr. B. Eckmann Eidgenossische Technische Hochschule Zurich Prof. Dr. B. L. van cler Waerclen Mathematisches Institut der Universitat ZUrich ISBN 978-3-642-86519-0 ISBN 978-3-642-86518-3 (eBook) DOl 10.1007/978-3-642-86518-3 Aile Rechte vorbehalten. Kein Teil dieses Buches darf ohne schriftliche Genehmigung des Springer-Verlages ubersetzt oder in irgendeiner Form vervielfaltigt werden © by Springer-Verlag Berlin· Heidelberg 1955 und 1969 (...)
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  • Issues in Epistemic and Modal Logics and Their Applications.Cezar A. Mortari - 1991 - Dissertation, University of Tübingen
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  • 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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  • Proof and truth: an anti-realist perspective.Luca Tranchini - 2013 - Pisa: Edizioni ETS. Edited by Luca Tranchini.
    In the first chapter, we discuss Dummett’s idea that the notion of truth arises from the one of the correctness of an assertion. We argue that, in a first-order language, the need of defining truth in terms of the notion of satisfaction, which is yielded by the presence of quantifiers, is structurally analogous to the need of a notion of truth as distinct from the one of correctness of an assertion. In the light of the analogy between predicates in Frege (...)
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  • Frege and the resolution calculus.Peter Schroeder-Heister - 1997 - History and Philosophy of Logic 18 (2):95-108.
    We reconstruct Frege’s treatment of certain deducibility problems posed by Boole. It turns out that in his formalization and solution of Boole’s problems Frege anticipates the idea of propositional resolution.
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  • (1 other version)Frege: Philosophy of Language.Michael Dummett - 1973 - London: Duckworth.
    This highly acclaimed book is a major contribution to the philosophy of language as well as a systematic interpretation of Frege, indisputably the father of ...
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  • Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
    This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.
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  • From simple associations to systematic reasoning: A connectionist representation of rules, variables, and dynamic binding using temporal synchrony.Lokendra Shastri & Venkat Ajjanagadde - 1993 - Behavioral and Brain Sciences 16 (3):417-51.
    Human agents draw a variety of inferences effortlessly, spontaneously, and with remarkable efficiency – as though these inferences were a reflexive response of their cognitive apparatus. Furthermore, these inferences are drawn with reference to a large body of background knowledge. This remarkable human ability seems paradoxical given the complexity of reasoning reported by researchers in artificial intelligence. It also poses a challenge for cognitive science and computational neuroscience: How can a system of simple and slow neuronlike elements represent a large (...)
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  • Foundations of Logic Programming.J. W. Lloyd - 1987 - Journal of Symbolic Logic 52 (1):288-289.
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  • Eight Rules for Implication Elimination.Michael Arndt - 2024 - In Thomas Piecha & Kai F. Wehmeier (eds.), Peter Schroeder-Heister on Proof-Theoretic Semantics. Springer. pp. 239-273.
    Eight distinct rules for implication in the antecedent for the sequent calculus, one of which being Gentzen’s standard rule, can be derived by successively applying a number of cuts to the logical ground sequent A → B, A ⇒ B. A naive translation into natural deduction collapses four of those rules onto the standard implication elimination rule, and the remaining four rules onto the general elimination rule. This collapse is due to the fact that the difference between a formula occurring (...)
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  • Formal Theories of Occurrences and Substitutions.René Gazzari - 2022 - Bulletin of Symbolic Logic 28 (2):261-263.
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  • Atomic Systems in Proof-Theoretic Semantics: Two Approaches.Peter Schroeder-Heister & Thomas Piecha - 2016 - In Ángel Nepomuceno Fernández, Olga Pombo Martins & Juan Redmond (eds.), Epistemology, Knowledge and the Impact of Interaction. Cham, Switzerland: Springer Verlag.
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  • How to Ekman a Crabbé-Tennant.Peter Schroeder-Heister & Luca Tranchini - 2018 - Synthese 199 (Suppl 3):617-639.
    Developing early results of Prawitz, Tennant proposed a criterion for an expression to count as a paradox in the framework of Gentzen’s natural deduction: paradoxical expressions give rise to non-normalizing derivations. Two distinct kinds of cases, going back to Crabbé and Tennant, show that the criterion overgenerates, that is, there are derivations which are intuitively non-paradoxical but which fail to normalize. Tennant’s proposed solution consists in reformulating natural deduction elimination rules in general form. Developing intuitions of Ekman we show that (...)
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  • (2 other versions)The Open Society and Its Enemies.K. R. Popper - 1946 - Philosophy 21 (80):271-276.
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  • A model-theoretic reconstruction of Frege's permutation argument.Peter Schroeder-Heister - 1987 - Notre Dame Journal of Formal Logic 28 (1):69-79.
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  • Intensional Harmony as Isomorphism.Paolo Pistone & Luca Tranchini - 2024 - In Thomas Piecha & Kai F. Wehmeier (eds.), Peter Schroeder-Heister on Proof-Theoretic Semantics. Springer. pp. 315-337.
    In the present paper we discuss a recent suggestion of Schroeder-Heister concerning the possibility of defining an intensional notion of harmony using isomorphism in second-order propositional logic. The latter is not an absolute notion, but its definition is relative to the choice of criteria for identity of proofs. In the paper, it is argued that in order to attain a satisfactory account of harmony, one has to consider a notion of identity stronger than the usual one (based on β- and (...)
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  • Sinn und Bedeutung in der Logik Gottlob Freges.Christian Thiel - 1965 - Meisenheim am Glan Hain,:
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  • Base-extension semantics for intuitionistic sentential logic.Tor Sandqvist - 2015 - Logic Journal of the IGPL 23 (5):719-731.
    Intuitionistic sentential logic is shown to be sound and complete with respect to a semantics centered around extensions of atomic bases (i.e. sets of inference rules for atomic sentences). The result is made possible through a non-standard interpretation of disjunction, whereby, roughly speaking, a disjunction is taken to hold just in case every atomic sentence that follows from each of the disjuncts separately holds; it is argued that this interpretation makes good sense provided that rules in atomic bases are conceived (...)
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  • (1 other version)12. Nicholas Rescher on Greek Philosophy and the Syllogism.Peter Schröder-Heister & Jürgen Mittelstraß - 2014 - In Jürgen Mittelstraß (ed.), Die Griechische Denkform: Von der Entstehung der Philosophie Aus Dem Geiste der Geometrie. Boston: De Gruyter. pp. 247-272.
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  • Completeness in Proof-Theoretic Semantics.Thomas Piecha - 2015 - In Peter Schroeder-Heister & Thomas Piecha (eds.), Advances in Proof-Theoretic Semantics. Cham, Switzerland: Springer Verlag.
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  • General Proof Theory: Introduction.Thomas Piecha & Peter Schroeder-Heister - 2019 - Studia Logica 107 (1):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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  • Bedeutung und psychischer Gehalt: eine Untersuchung zur sprachanalytischen Kritik von Husserls früher Phänomenologie.Gianfranco Soldati - 1994
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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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  • Conservativeness and uniqueness.Peter Schroeder-Heister - 1985 - Theoria 51 (3):159-173.
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  • Logical constants as punctuation marks.Kosta Došen - 1989 - Notre Dame Journal of Formal Logic 30 (3):362-381.
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  • Ekman’s Paradox.Peter Schroeder-Heister & Luca Tranchini - 2017 - Notre Dame Journal of Formal Logic 58 (4):567-581.
    Prawitz observed that Russell’s paradox in naive set theory yields a derivation of absurdity whose reduction sequence loops. Building on this observation, and based on numerous examples, Tennant claimed that this looping feature, or more generally, the fact that derivations of absurdity do not normalize, is characteristic of the paradoxes. Striking results by Ekman show that looping reduction sequences are already obtained in minimal propositional logic, when certain reduction steps, which are prima facie plausible, are considered in addition to the (...)
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  • A proof-theoretic approach to entailment.N. Tennant - 1980 - Journal of Philosophical Logic 9 (2):185 - 209.
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  • (2 other versions)Kant und das Problem der „Dinge an sich”.Gerold Prauss - 1975 - Tijdschrift Voor Filosofie 37 (2):339-340.
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  • Bibliographie Hugo Dingler.[author unknown] - 1981 - Zeitschrift für Philosophische Forschung 35 (2):283-298.
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  • Reduction, representation and commensurability of theories.Peter Schroeder-Heister & Frank Schaefer - 1989 - Philosophy of Science 56 (1):130-157.
    Theories in the usual sense, as characterized by a language and a set of theorems in that language ("statement view"), are related to theories in the structuralist sense, in turn characterized by a set of potential models and a subset thereof as models ("non-statement view", J. Sneed, W. Stegmüller). It is shown that reductions of theories in the structuralist sense (that is, functions on structures) give rise to so-called "representations" of theories in the statement sense and vice versa, where representations (...)
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