12 found

Year:

  1.  15
    Gödel on Deduction.Kosta Došen & Miloš Adžić - 2019 - Studia Logica 107 (1):31-51.
    This is an examination, a commentary, of links between some philosophical views ascribed to Gödel and general proof theory. In these views deduction is of central concern not only in predicate logic, but in set theory too, understood from an infinitistic ideal perspective. It is inquired whether this centrality of deduction could also be kept in the intensional logic of concepts whose building Gödel seems to have taken as the main task of logic for the future.
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  2.  9
    Proof Compression and NP Versus PSPACE.L. Gordeev & E. H. Haeusler - 2019 - Studia Logica 107 (1):53-83.
    We show that arbitrary tautologies of Johansson’s minimal propositional logic are provable by “small” polynomial-size dag-like natural deductions in Prawitz’s system for minimal propositional logic. These “small” deductions arise from standard “large” tree-like inputs by horizontal dag-like compression that is obtained by merging distinct nodes labeled with identical formulas occurring in horizontal sections of deductions involved. The underlying geometric idea: if the height, h(∂), and the total number of distinct formulas, ϕ(∂), of a given tree-like deduction ∂ of a minimal (...)
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  3.  9
    Logicality, Double-Line Rules, and Modalities.Norbert Gratzl & Eugenio Orlandelli - 2019 - Studia Logica 107 (1):85-107.
    This paper deals with the question of the logicality of modal logics from a proof-theoretic perspective. It is argued that if Dos̆en’s analysis of logical constants as punctuation marks is embraced, it is possible to show that all the modalities in the cube of normal modal logics are indeed logical constants. It will be proved that the display calculus for each displayable modality admits a purely structural presentation based on double-line rules which, following Dos̆en’s analysis, allows us to claim that (...)
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  4.  5
    Postponement of $$\Mathsf {Raa}$$ Raa and Glivenko’s Theorem, Revisited.Giulio Guerrieri & Alberto Naibo - 2019 - Studia Logica 107 (1):109-144.
    We study how to postpone the application of the reductio ad absurdum rule in classical natural deduction. This technique is connected with two normalization strategies for classical logic, due to Prawitz and Seldin, respectively. We introduce a variant of Seldin’s strategy for the postponement of $$\mathsf {raa}$$ raa, which induces a negative translation from classical to intuitionistic and minimal logic. Through this translation, Glivenko’s theorem from classical to intuitionistic and minimal logic is proven.
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  5.  1
    Postponement of $$Mathsf {}$$ and Glivenko’s Theorem, Revisited.Giulio Guerrieri & Alberto Naibo - 2019 - Studia Logica 107 (1):109-144.
    We study how to postpone the application of the reductio ad absurdum rule ) in classical natural deduction. This technique is connected with two normalization strategies for classical logic, due to Prawitz and Seldin, respectively. We introduce a variant of Seldin’s strategy for the postponement of \, which induces a negative translation from classical to intuitionistic and minimal logic. Through this translation, Glivenko’s theorem from classical to intuitionistic and minimal logic is proven.
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  6.  16
    Is There a “Hilbert Thesis”?Reinhard Kahle - 2019 - Studia Logica 107 (1):145-165.
    In his introductory paper to first-order logic, Jon Barwise writes in the Handbook of Mathematical Logic :[T]he informal notion of provable used in mathematics is made precise by the formal notion provable in first-order logic. Following a sug[g]estion of Martin Davis, we refer to this view as Hilbert’s Thesis.This paper reviews the discussion of Hilbert’s Thesis in the literature. In addition to the question whether it is justifiable to use Hilbert’s name here, the arguments for this thesis are compared with (...)
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  7.  9
    Inference as Doxastic Agency. Part I: The Basics of Justification Stit Logic.Grigory K. Olkhovikov & Heinrich Wansing - 2019 - Studia Logica 107 (1):167-194.
    In this paper we consider logical inference as an activity that results in proofs and hence produces knowledge. We suggest to merge the semantical analysis of deliberatively seeing-to-it-that from stit theory and the semantics of the epistemic logic with justification from. The general idea is to understand proving that A as seeing to it that a proof of A is available. We introduce a semantics of various notions of proving as an activity and present a number of valid principles that (...)
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  8.  10
    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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  9.  16
    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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  10.  24
    The Fundamental Problem of General Proof Theory.Dag Prawitz - 2019 - Studia Logica 107 (1):11-29.
    I see the question what it is that makes an inference valid and thereby gives a proof its epistemic power as the most fundamental problem of general proof theory. It has been surprisingly neglected in logic and philosophy of mathematics with two exceptions: Gentzen’s remarks about what justifies the rules of his system of natural deduction and proposals in the intuitionistic tradition about what a proof is. They are reviewed in the paper and I discuss to what extent they succeed (...)
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  11.  6
    Kosta Došen.Peter Schroeder-Heister - 2019 - Studia Logica 107 (1):7-9.
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  12.  15
    The Naturality of Natural Deduction.Luca Tranchini, Paolo Pistone & Mattia Petrolo - 2019 - Studia Logica 107 (1):195-231.
    Developing a suggestion by Russell, Prawitz showed how the usual natural deduction inference rules for disjunction, conjunction and absurdity can be derived using those for implication and the second order quantifier in propositional intuitionistic second order logic NI\. It is however well known that the translation does not preserve the relations of identity among derivations induced by the permutative conversions and immediate expansions for the definable connectives, at least when the equational theory of NI\ is assumed to consist only of (...)
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