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Peter Schroeder-Heister [32]Peter Joseph Schroeder-Heister [4]
  1.  22
    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.  9
    On Flattening Elimination Rules.Grigory K. Olkhovikov & Peter Schroeder-Heister - 2014 - Review of Symbolic Logic 7 (1):60-72.
  4.  34
    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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  5.  36
    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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  6.  24
    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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  7.  13
    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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  8.  96
    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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  9.  24
    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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  10.  77
    Introduction: Proof-Theoretic Semantics.Reinhard Kahle & Peter Schroeder-Heister - 2006 - Synthese 148 (3):503-506.
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  11. Uniqueness, Definability and Interpolation.Kosta Došen & Peter Schroeder-Heister - 1988 - Journal of Symbolic Logic 53 (2):554-570.
  12.  51
    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.  25
    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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  14. Substructural Logics.Peter Joseph Schroeder-Heister, Kosta Dosen & Seminar Für Natürlich-Sprachliche Systeme - 1993
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  15.  3
    Ekman’s Paradox.Peter Schroeder-Heister & Luca Tranchini - forthcoming - Notre Dame Journal of Formal Logic.
    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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  16. Introduction to Proof Theoretic Semantics. Special Issue Of.Reinhard Kahle & Peter Schroeder-Heister - 2006 - Synthese 148.
     
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  17. Uniform Proof-Theoretic Semantics for Logical Constants.Peter Schroeder-Heister - 1991 - Journal of Symbolic Logic 56:1142.
  18.  16
    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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  19.  67
    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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  20.  49
    Book Note. [REVIEW]Ulf Friedrichsdorf & Peter Schroeder-Heister - 1985 - Journal of Semantics 4 (4):389-390.
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  21.  7
    A Model-Theoretic Reconstruction of Frege's Permutation Argument.Peter Schroeder-Heister - 1987 - Notre Dame Journal of Formal Logic 28 (1):69-79.
  22.  30
    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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  23.  40
    Conservativeness and Uniqueness.Peter Schroeder-Heister - 1985 - Theoria 51 (3):159-173.
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  24.  52
    Frege's Permutation Argument Revisited.Kai Frederick Wehmeier & Peter Schroeder-Heister - 2005 - Synthese 147 (1):43 - 61.
    any other one with the False, without contradicting any stipulations previously introduced (we shall call this claim the identiability thesis, following Schroeder-Heister [13]). As far as we are aware, there is no consensus in the literature as to (i) the proper interpretation of the permutation argument and the identiability thesis, (ii) the validity of the permutation argument, and (iii) the truth of the identiability thesis.1 In this paper, we undertake a detailed technical study of the two main lines of interpretation, (...)
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  25.  18
    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.
  26.  8
    Frege’s Permutation Argument Revisited.Kai Frederick Wehmeier & Peter Schroeder-Heister - 2005 - Synthese 147 (1):43-61.
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  27.  23
    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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  28.  5
    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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  29.  2
    14th Congress of Logic, Methodology and Philosophy of Science.Gerhard Heinzmann & Peter Schroeder-Heister - 2008 - Philosophia Scientiae 14 (1):155-157.
  30.  2
    Review: Wolfgang Schuler, Grundlegungen der Mathematik in Transzendentaler Kritik. Frege und Hilbert. [REVIEW]Peter Schroeder-Heister - 1989 - Journal of Symbolic Logic 54 (2):622-622.
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  31. Extensions of Logic Programming 5th International Workshop, Elp '96, Leipzig, Germany, March 28-30, 1996 : Proceedings'.Roy Dyckhoff, Heinrich Herre & Peter Joseph Schroeder-Heister - 1996
     
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  32. Extensions of Logic Programming Second International Workshop, Elp '91, Stockholm, Sweden, January 27-29, 1991 : Proceedings. [REVIEW]L. Eriksson, Lars Hallnäs, Peter Joseph Schroeder-Heister & Elp '91 - 1992
     
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  33. Begründungsrationalität und Logik.Peter Schroeder-Heister - 2005 - In Gereon Wolters & Martin Carrier (eds.), Homo Sapiens Und Homo Faber. De Gruyter. pp. 285--296.
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  34. Substructural Logics.Peter Schroeder-Heister - 1996 - Erkenntnis 45 (1):115-118.
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  35. Schüler Wolfgang. Grundlegungen der Mathematik in transzendentaler Kritik, Frege und Hilbert, Schriften zur Transzendentalphilosophie, vol. 3, Felix Meiner Verlag, Hamburg 1983, xv + 190 pp. [REVIEW]Peter Schroeder-Heister - 1989 - Journal of Symbolic Logic 54 (2):622.
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