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Peter Schroeder-Heister [47]Peter Joseph Schroeder-Heister [1]
  1. (1 other version)Proof-Theoretic Semantics.Peter Schroeder-Heister - forthcoming - Stanford Encyclopedia of Philosophy.
  2. 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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  3. Validity Concepts in Proof-theoretic Semantics.Peter Schroeder-Heister - 2006 - Synthese 148 (3):525-571.
    The standard approach to what I call “proof-theoretic semantics”, which is mainly due to Dummett and Prawitz, attempts to give a semantics of proofs by defining what counts as a valid proof. After a discussion of the general aims of proof-theoretic semantics, this paper investigates in detail various notions of proof-theoretic validity and offers certain improvements of the definitions given by Prawitz. Particular emphasis is placed on the relationship between semantic validity concepts and validity concepts used in normalization theory. It (...)
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  4.  46
    Advances in Proof-Theoretic Semantics.Peter Schroeder-Heister & Thomas Piecha (eds.) - 2015 - Cham, Switzerland: Springer Verlag.
    This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory. The field of proof-theoretic semantics has existed for almost 50 years, but the term (...)
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  5.  35
    Substructural Logics.Peter Joseph Schroeder-Heister & Kosta Došen - 1993 - Oxford, England: Oxford University Press on Demand.
    The new area of logic and computation is now undergoing rapid development. This has affected the social pattern of research in the area. A new topic may rise very quickly with a significant body of research around it. The community, however, cannot wait the traditional two years for a book to appear. This has given greater importance to thematic collections of papers, centred around a topic and addressing it from several points of view, usually as a result of a workshop, (...)
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  6.  43
    Incompleteness of Intuitionistic Propositional Logic with Respect to Proof-Theoretic Semantics.Thomas Piecha & Peter Schroeder-Heister - 2019 - Studia Logica 107 (1):233-246.
    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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  7.  47
    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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  8.  88
    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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  9.  88
    The categorical and the hypothetical: a critique of some fundamental assumptions of standard semantics.Peter Schroeder-Heister - 2012 - Synthese 187 (3):925-942.
    The hypothetical notion of consequence is normally understood as the transmission of a categorical notion from premisses to conclusion. In model-theoretic semantics this categorical notion is 'truth', in standard proof-theoretic semantics it is 'canonical provability'. Three underlying dogmas, (I) the priority of the categorical over the hypothetical, (II) the transmission view of consequence, and (III) the identification of consequence and correctness of inference are criticized from an alternative view of proof-theoretic semantics. It is argued that consequence is a basic semantical (...)
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  10.  40
    On flattening elimination rules.Grigory K. Olkhovikov & Peter Schroeder-Heister - 2014 - Review of Symbolic Logic 7 (1):60-72.
  11.  39
    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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  12.  98
    Proof-Theoretic Semantics, Self-Contradiction, and the Format of Deductive Reasoning.Peter Schroeder-Heister - 2012 - Topoi 31 (1):77-85.
    From the point of view of proof-theoretic semantics, it is argued that the sequent calculus with introduction rules on the assertion and on the assumption side represents deductive reasoning more appropriately than natural deduction. In taking consequence to be conceptually prior to truth, it can cope with non-well-founded phenomena such as contradictory reasoning. The fact that, in its typed variant, the sequent calculus has an explicit and separable substitution schema in form of the cut rule, is seen as a crucial (...)
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  13. Uniform proof-theoretic semantics for logical constants.Peter Schroeder-Heister - 1991 - Journal of Symbolic Logic 56:1142.
  14. Generalized definitional reflection and the inversion principle.Peter Schroeder-Heister - 2007 - Logica Universalis 1 (2):355-376.
    . The term inversion principle goes back to Lorenzen who coined it in the early 1950s. It was later used by Prawitz and others to describe the symmetric relationship between introduction and elimination inferences in natural deduction, sometimes also called harmony. In dealing with the invertibility of rules of an arbitrary atomic production system, Lorenzen’s inversion principle has a much wider range than Prawitz’s adaptation to natural deduction. It is closely related to definitional reflection, which is a principle for reasoning (...)
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  15.  68
    The Calculus of Higher-Level Rules, Propositional Quantification, and the Foundational Approach to Proof-Theoretic Harmony.Peter Schroeder-Heister - 2014 - Studia Logica 102 (6):1185-1216.
    We present our calculus of higher-level rules, extended with propositional quantification within rules. This makes it possible to present general schemas for introduction and elimination rules for arbitrary propositional operators and to define what it means that introductions and eliminations are in harmony with each other. This definition does not presuppose any logical system, but is formulated in terms of rules themselves. We therefore speak of a foundational account of proof-theoretic harmony. With every set of introduction rules a canonical elimination (...)
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  16. Introduction: Proof-theoretic semantics.Reinhard Kahle & Peter Schroeder-Heister - 2006 - Synthese 148 (3):503-506.
  17. Definitional Reflection and Basic Logic.Peter Schroeder-Heister - 2013 - Annals of Pure and Applied Logic 164 (4):491-501.
    In their Basic Logic, Sambin, Battilotti and Faggian give a foundation of logical inference rules by reference to certain reflection principles. We investigate the relationship between these principles and the principle of Definitional Reflection proposed by Hallnäs and Schroeder-Heister.
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  18.  94
    Resolution and the origins of structural reasoning: Early proof-theoretic ideas of Hertz and Gentzen.Peter Schroeder-Heister - 2002 - Bulletin of Symbolic Logic 8 (2):246-265.
    In the 1920s, Paul Hertz (1881-1940) developed certain calculi based on structural rules only and established normal form results for proofs. It is shown that he anticipated important techniques and results of general proof theory as well as of resolution theory, if the latter is regarded as a part of structural proof theory. Furthermore, it is shown that Gentzen, in his first paper of 1933, which heavily draws on Hertz, proves a normal form result which corresponds to the completeness of (...)
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  19. Substructural Logics.Peter Schroeder-Heister - 1996 - Erkenntnis 45 (1):115-118.
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  20. Conservativeness and uniqueness.Peter Schroeder-Heister - 1985 - Theoria 51 (3):159-173.
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  21.  59
    A model-theoretic reconstruction of Frege's permutation argument.Peter Schroeder-Heister - 1987 - Notre Dame Journal of Formal Logic 28 (1):69-79.
  22. 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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  23.  58
    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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  24. Uniqueness, definability and interpolation.Kosta Došen & Peter Schroeder-Heister - 1988 - Journal of Symbolic Logic 53 (2):554-570.
  25.  74
    Popper's theory of deductive inference and the concept of a logical constant.Peter Schroeder-Heister - 1984 - History and Philosophy of Logic 5 (1):79-110.
    This paper deals with Popper's little-known work on deductive logic, published between 1947 and 1949. According to his theory of deductive inference, the meaning of logical signs is determined by certain rules derived from ?inferential definitions? of those signs. Although strong arguments have been presented against Popper's claims (e.g. by Curry, Kleene, Lejewski and McKinsey), his theory can be reconstructed when it is viewed primarily as an attempt to demarcate logical from non-logical constants rather than as a semantic foundation for (...)
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  26.  86
    Frege’s permutation argument revisited.Kai Frederick Wehmeier & Peter Schroeder-Heister - 2005 - Synthese 147 (1):43-61.
    In Section 10 of Grundgesetze, Volume I, Frege advances a mathematical argument (known as the permutation argument), by means of which he intends to show that an arbitrary value-range may be identified with the True, and any other one with the False, without contradicting any stipulations previously introduced (we shall call this claim the identifiability thesis, following Schroeder-Heister (1987)). As far as we are aware, there is no consensus in the literature as to (i) the proper interpretation of the permutation (...)
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  27. 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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  28.  64
    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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  29.  63
    The completeness of intuitionistic logic with respect to a validity concept based on an inversion principle.Peter Schroeder-Heister - 1983 - Journal of Philosophical Logic 12 (3):359 - 377.
  30. Introduction to Proof Theoretic Semantics. Special issue of.Reinhard Kahle & Peter Schroeder-Heister - 2006 - Synthese 148.
  31.  29
    Kosta Došen.Peter Schroeder-Heister - 2019 - Studia Logica 107 (1):7-9.
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  32.  23
    Enzyklopädie Philosophie und Wissenschaftstheorie: Band 1: A–B.Gottfried Gabriel, Matthias Gatzemeier, Carl F. Gethmann, Peter Janich, Friedrich Kambartel, Kuno Lorenz, Klaus Mainzer, Peter Schroeder-Heister, Christian Thiel, Reiner Wimmer & Martin Carrier - 2024 - Springer Berlin Heidelberg.
    Die »Enzyklopädie Philosophie- und Wissenschaftstheorie«, das größte allgemeine Nachschlagewerk zur Philosophie im deutschsprachigen Raum, wurde 1980 begonnen und 1996 mit dem vierten Band abgeschlossen. Sie erschien 2005 bis 2018 in einer komplett aktualisierten und erweiterten 8-bändigen Neuauflage, die hiermit nun in einer kartonierten Sonderausgabe vorliegt. Die »Enzyklopädie« umfasst in Sach- und Personenartikeln nicht nur den klassischen Bestand des philosophischen Wissens, sondern auch die neuere Entwicklung der Philosophie, insbesondere in den Bereichen Logik, Erkenntnis- und Wissenschaftstheorie sowie Sprachphilosophie. Zugleich finden Grundlagenreflexionen in (...)
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  33.  33
    14th Congress of Logic, Methodology and Philosophy of Science.Gerhard Heinzmann & Peter Schroeder-Heister - 2008 - Philosophia Scientiae 14 (1):155-157.
  34.  11
    Nicholas Rescher on Greek Philosophy and the Syllogism.Jürgen Mittelstrass & Peter Schroeder-Heister - 2008 - In Robert Almeder (ed.), Rescher Studies: A Collection of Essays on the Philosophical Work of Nicholas Rescher. De Gruyter. pp. 211-240.
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  35.  35
    Recent frege studies.Peter Schroeder-Heister & Rezensiert Von Gottfried Gabriel - 1983 - History and Philosophy of Logic 4 (1-2):99-106.
    MICHAEL D. RESNIK, Frege and the philosophy of mathematics. Ithaca and London: Cornell University Press, 1980. 244 pp. $16.50. HANS D. SLUGA, Gottlob Frege. London, Boston and Henley: Routledge & Kegan Paul, 1980. xi + 203 pp. £ 12.95.
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  36. Advances in Proof-Theoretic Semantics: Introduction.Peter Schroeder-Heister & Thomas Piecha - 2015 - In Peter Schroeder-Heister & Thomas Piecha (eds.), Advances in Proof-Theoretic Semantics. Cham, Switzerland: Springer Verlag.
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  37.  18
    Begründungsrationalität und Logik.Peter Schroeder-Heister - 2005 - In Gereon Wolters & Martin Carrier (eds.), Homo Sapiens und Homo Faber: epistemische und technische Rationalität in Antike und Gegenwart ; Festschrift für Jürgen Mittelstrass. Berlin/New York: de Gruyter. pp. 285--296.
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  38.  5
    Comments on the Contributions.Peter Schroeder-Heister - 2024 - In Thomas Piecha & Kai F. Wehmeier (eds.), Peter Schroeder-Heister on Proof-Theoretic Semantics. Springer. pp. 443-455.
    The contributions to this volume represent a broad range of aspects of proof-theoretic semantics. Some do so in the narrower, and some in the wider sense of the term. Some deal with issues I have been concerned with directly, and some tackle further problems. All of them open interesting new perspectives and develop the field in different directions. I will briefly comment on the significance of each contribution here.
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  39.  9
    Extensions of Logic Programming: International Workshop, Tübingen, FRG, December 8-10, 1989. Proceedings.Peter Schroeder-Heister - 1991 - Springer.
    This volume contains finalized versions of papers presented at an international workshop on extensions of logic programming, held at the Seminar for Natural Language Systems at the University of Tübingen in December 1989. Several recent extensions of definite Horn clause programming, especially those with a proof-theoretic background, have much in common. One common thread is a new emphasis on hypothetical reasoning, which is typically inspired by Gentzen-style sequent or natural deduction systems. This is not only of theoretical significance, but also (...)
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  40. Logic, Methodology and Philosophy of Science, Proceedings of the 14th International Congress.Peter Schroeder-Heister, Gerhard Heinzmann, Wilfred Hodges & Pierre Edouard Bour (eds.) - 2014 - London, UK:
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  41. Open Problems in Proof-Theoretic Semantics.Peter Schroeder-Heister - 2015 - In Peter Schroeder-Heister & Thomas Piecha (eds.), Advances in Proof-Theoretic Semantics. Cham, Switzerland: Springer Verlag.
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  42. Prawitz's completeness conjecture: A reassessment.Peter Schroeder-Heister - forthcoming - Theoria.
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  43.  5
    (1 other version)9 Wahrscheinlichkeit.Peter Schroeder-Heister - 1935 - In Karl R. Popper (ed.), Logik der Forschung. Wien: Springer. pp. 187-215.
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  44.  69
    Implications-as-Rules vs. Implications-as-Links: An Alternative Implication-Left Schema for the Sequent Calculus. [REVIEW]Peter Schroeder-Heister - 2011 - Journal of Philosophical Logic 40 (1):95 - 101.
    The interpretation of implications as rules motivates a different left-introduction schema for implication in the sequent calculus, which is conceptually more basic than the implication-left schema proposed by Gentzen. Corresponding to results obtained for systems with higher-level rules, it enjoys the subformula property and cut elimination in a weak form.
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  45.  8
    Extensions of Logic Programming: 5th International Workshop, Elp '96, Leipzig, Germany, March 28 - 30, 1996. Proceedings.Roy Dyckhoff, Heinrich Herre & Peter Schroeder-Heister - 1996 - Springer Verlag.
    A major strategy to reduce transport congestion and other social costs of transport is to ensure that travellers make the best decisions, based on real time information. A wide range of technological systems have been developed to provide this information, but little is known about how travellers actually respond to it. This book offers an overview of various transport telematics options and provides an appropriate methodological framework, followed by a presentation of results from actual applications of these telematics systems from (...)
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  46.  21
    Wolfgang Schüler. Grundlegungen der Mathematik in transzendentaler Kritik, Frege und Hilbert, Schriften zur Transzendentalphilosophie, vol. 3, Felix Meiner Verlag, Hamburg1983, xv + 190 pp. [REVIEW]Peter Schroeder-Heister - 1989 - Journal of Symbolic Logic 54 (2):622.
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