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  1. Grigory K. Olkhovikov & Peter Schroeder-Heister (forthcoming). On Flattening Elimination Rules. Review of Symbolic Logic:1-13.
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  2. Peter Schroeder-Heister (forthcoming). Proof-Theoretic Semantics. Stanford Encyclopedia of Philosophy.
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  3. Peter Schroeder-Heister (2013). Definitional Reflection and Basic Logic. Annals of Pure and Applied Logic 164 (4):491-501.
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  4. Peter Schroeder-Heister (2012). Proof-Theoretic Semantics, Self-Contradiction, and the Format of Deductive Reasoning. 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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  5. Peter Schroeder-Heister (2012). The Categorical and the Hypothetical: A Critique of Some Fundamental Assumptions of Standard Semantics. 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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  6. Peter Schroeder-Heister (2011). Implications-as-Rules Vs. Implications-as-Links: An Alternative Implication-Left Schema for the Sequent Calculus. [REVIEW] 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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  7. Gerhard Heinzmann & Peter Schroeder-Heister (2008). 14th Congress of Logic, Methodology and Philosophy of Science. Philosophia Scientiae 14:155-157.
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  8. Peter Schroeder-Heister (2007). Generalized Definitional Reflection and the Inversion Principle. 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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  9. Reinhard Kahle & Peter Schroeder-Heister (2006). Introduction: Proof-Theoretic Semantics. Synthese 148 (3):503-506.
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  10. Reinhard Kahle & Peter Schroeder-Heister (2006). Introduction to Proof Theoretic Semantics. Special Issue Of. Synthese 148.
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  11. Peter Schroeder-Heister (2006). Validity Concepts in Proof-Theoretic Semantics. 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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  12. Peter Schroeder-Heister (2005). Begründungsrationalität und Logik. In Gereon Wolters & Martin Carrier (eds.), Homo Sapiens Und Homo Faber. De Gruyter. 285--296.
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  13. Kai Frederick Wehmeier & Peter Schroeder-Heister (2005). Frege's Permutation Argument Revisited. 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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  14. Peter Schroeder-Heister (2002). Resolution and the Origins of Structural Reasoning: Early Proof-Theoretic Ideas of Hertz and Gentzen. 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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  15. Peter Schroeder-Heister (1997). Frege and the Resolution Calculus. 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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  16. Peter Schroeder-Heister (1991). Uniform Proof-Theoretic Semantics for Logical Constants. Journal of Symbolic Logic 56:1142.
     
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  17. Peter Schroeder-Heister (1989). Review: Wolfgang Schuler, Grundlegungen der Mathematik in Transzendentaler Kritik. Frege und Hilbert. [REVIEW] Journal of Symbolic Logic 54 (2):622-622.
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  18. Peter Schroeder-Heister & Frank Schaefer (1989). Reduction, Representation and Commensurability of Theories. 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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  19. Kosta Došen & Peter Schroeder-Heister (1988). Uniqueness, Definability and Interpolation. Journal of Symbolic Logic 53 (2):554-570.
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  20. Peter Schroeder-Heister (1987). A Model-Theoretic Reconstruction of Frege's Permutation Argument. Notre Dame Journal of Formal Logic 28 (1):69-79.
  21. Ulf Friedrichsdorf & Peter Schroeder-Heister (1985). Book Note. [REVIEW] Journal of Semantics 4 (4):389-390.
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  22. Peter Schroeder-Heister (1985). Conservativeness and Uniqueness. Theoria 51 (3):159-173.
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  23. Peter Schroeder-Heister (1984). Popper's Theory of Deductive Inference and the Concept of a Logical Constant. 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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  24. Peter Schroeder-Heister (1984). A Natural Extension of Natural Deduction. 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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  25. Peter Schroeder-Heister (1983). The Completeness of Intuitionistic Logic with Respect to a Validity Concept Based on an Inversion Principle. Journal of Philosophical Logic 12 (3):359 - 377.
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  26. Peter Schroeder-Heister & Rezensiert Von Gottfried Gabriel (1983). Recent Frege Studies. 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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