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Advances in Proof-Theoretic Semantics

Cham, Switzerland: Springer Verlag (2015)

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  1. (1 other version)Inquiries Into Truth And Interpretation.Donald Davidson - 1984 - Oxford, GB: Oxford University Press.
    Now in a new edition, this volume updates Davidson's exceptional Inquiries into Truth and Interpretation (1984), which set out his enormously influential philosophy of language. The original volume remains a central point of reference, and a focus of controversy, with its impact extending into linguistic theory, philosophy of mind, and epistemology. Addressing a central question--what it is for words to mean what they do--and featuring a previously uncollected, additional essay, this work will appeal to a wide audience of philosophers, linguists, (...)
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  • 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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  • The logical basis of metaphysics.Michael Dummett - 1991 - Cambridge: Harvard University Press.
    Such a conception, says Dummett, will form "a base camp for an assault on the metaphysical peaks: I have no greater ambition in this book than to set up a base ...
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  • Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
    A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.
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  • (2 other versions)Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
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  • (5 other versions)Uber Sinn und Bedeutung.Gottlob Frege - 1892 - Zeitschrift für Philosophie Und Philosophische Kritik 100 (1):25-50.
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  • The concept of truth in formalized languages.Alfred Tarski - 1956 - In Logic, semantics, metamathematics. Oxford,: Clarendon Press. pp. 152--278.
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  • Articulating Reasons: An Introduction to Inferentialism.Robert Brandom - 2002 - Philosophical Quarterly 52 (206):123-125.
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  • Intuitionistic Type Theory.Per Martin-Löf - 1980 - Bibliopolis.
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  • Die Grundlagen der Arithmetik. Eine logisch mathematische Untersuchung über den Begriff der Zahl.Gottlob Frege - 1884 - Wittgenstein-Studien 3 (2):993-999.
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  • Foundations of Set Theory.Abraham Adolf Fraenkel & Yehoshua Bar-Hillel - 1973 - Atlantic Highlands, NJ, USA: Elsevier.
    Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of (...)
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  • Tonk, Plonk and Plink.Nuel Belnap - 1962 - Analysis 22 (6):130-134.
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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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  • Symbolic logic.Frederic Brenton Fitch - 1952 - New York,: Ronald Press Co..
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  • (1 other version)Semantical Analysis of Intuitionistic Logic I.Saul A. Kripke - 1963 - In Michael Dummett & J. N. Crossley (eds.), Formal Systems and Recursive Functions. Amsterdam,: North Holland. pp. 92-130.
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  • Explicit provability and constructive semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.
    In 1933 Godel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that Godel's provability calculus is nothing but the forgetful projection of LP. This also achieves Godel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a Brouwer-Heyting-Kolmogorov style provability semantics for Int which (...)
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  • Introduction to Higher Order Categorical Logic.J. Lambek & P. J. Scott - 1989 - Journal of Symbolic Logic 54 (3):1113-1114.
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  • (1 other version)Proof-Theoretic Semantics.Peter Schroeder-Heister - forthcoming - Stanford Encyclopedia of Philosophy.
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  • New Essays on the Knowability Paradox.Joe Salerno (ed.) - 2008 - Oxford, England and New York, NY, USA: Oxford University Press.
    This collection assembles Church's referee reports, Fitch's 1963 paper, and nineteen new papers on the knowability paradox.
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  • A paradox regained.D. Kaplan & R. Montague - 1960 - Notre Dame Journal of Formal Logic 1 (3):79-90.
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  • Meaning Approached Via Proofs.Dag Prawitz - 2006 - Synthese 148 (3):507-524.
    According to a main idea of Gentzen the meanings of the logical constants are reflected by the introduction rules in his system of natural deduction. This idea is here understood as saying roughly that a closed argument ending with an introduction is valid provided that its immediate subarguments are valid and that other closed arguments are justified to the extent that they can be brought to introduction form. One main part of the paper is devoted to the exact development of (...)
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  • On the meanings of the logical constants and the justifications of the logical laws.Per Martin-Löf - 1996 - Nordic Journal of Philosophical Logic 1 (1):11–60.
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  • Logische Untersuchungen (Hrsg. v. Günther Patzig).Gottlob Frege - 1976 - Göttingen: Vandenhoeck und Ruprecht.
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  • Harmony and autonomy in classical logic.Stephen Read - 2000 - Journal of Philosophical Logic 29 (2):123-154.
    Michael Dummett and Dag Prawitz have argued that a constructivist theory of meaning depends on explicating the meaning of logical constants in terms of the theory of valid inference, imposing a constraint of harmony on acceptable connectives. They argue further that classical logic, in particular, classical negation, breaks these constraints, so that classical negation, if a cogent notion at all, has a meaning going beyond what can be exhibited in its inferential use. I argue that Dummett gives a mistaken elaboration (...)
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  • 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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  • On the idea of a general proof theory.Dag Prawitz - 1974 - Synthese 27 (1-2):63 - 77.
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  • Semantical Investigations in Heyting's Intuitionistic Logic.Dov M. Gabbay - 1986 - Journal of Symbolic Logic 51 (3):824-824.
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  • Knowledge and its Limits. [REVIEW]L. Horsten - 2000 - Tijdschrift Voor Filosofie 64 (1):200-201.
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  • Proof-Theoretic Semantics for Subsentential Phrases.Nissim Francez, Roy Dyckhoff & Gilad Ben-Avi - 2010 - Studia Logica 94 (3):381-401.
    The paper briefly surveys the sentential proof-theoretic semantics for fragment of English. Then, appealing to a version of Frege’s context-principle (specified to fit type-logical grammar), a method is presented for deriving proof-theoretic meanings for sub-sentential phrases, down to lexical units (words). The sentential meaning is decomposed according to the function-argument structure as determined by the type-logical grammar. In doing so, the paper presents a novel proof-theoretic interpretation of simple type, replacing Montague’s model-theoretic type interpretation (in arbitrary Henkin models). The domains (...)
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  • Victor's error.Michael Dummett - 2001 - Analysis 61 (1):1–2.
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  • Towards a Foundation of General Proof Theory.Dag Prawitz - 1973 - In ¸ Itetsuppes1973. North Holland, Amsterdam.
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  • Constructions, proofs and the meaning of logical constants.Göran Sundholm - 1983 - Journal of Philosophical Logic 12 (2):151 - 172.
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  • Proof-theoretic semantics for a natural language fragment.Nissim Francez & Roy Dyckhoff - 2010 - Linguistics and Philosophy 33 (6):447-477.
    The paper presents a proof-theoretic semantics (PTS) for a fragment of natural language, providing an alternative to the traditional model-theoretic (Montagovian) semantics (MTS), whereby meanings are truth-condition (in arbitrary models). Instead, meanings are taken as derivability-conditions in a dedicated natural-deduction (ND) proof-system. This semantics is effective (algorithmically decidable), adhering to the meaning as use paradigm, not suffering from several of the criticisms formulated by philosophers of language against MTS as a theory of meaning. In particular, Dummett’s manifestation argument does not (...)
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  • How to Live Without Identity—And Why.Kai F. Wehmeier - 2012 - Australasian Journal of Philosophy 90 (4):761 - 777.
    Identity, we're told, is the binary relation that every object bears to itself, and to itself only. But how can a relation be binary if it never relates two objects? This puzzled Russell and led Wittgenstein to declare that identity is not a relation between objects. The now standard view is that Wittgenstein's position is untenable, and that worries regarding the relational status of identity are the result of confusion. I argue that the rejection of identity as a binary relation (...)
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  • .Joe Salerno - 2008 - In New Essays on the Knowability Paradox. Oxford, England and New York, NY, USA: Oxford University Press.
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  • Eine Unableitbarkeitsbeweismethode für den intuitionistischen Aussagenkalkul.G. Kreisel - 1957 - Archive for Mathematical Logic 3 (3-4):74.
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  • Proof-theoretic semantics, paradoxes and the distinction between sense and denotation.Luca Tranchini - forthcoming - Journal of Logic and Computation 2014.
    In this paper we show how Dummett-Prawitz-style proof-theoretic semantics has to be modified in order to cope with paradoxical phenomena. It will turn out that one of its basic tenets has to be given up, namely the definition of the correctness of an inference as validity preservation. As a result, the notions of an argument being valid and of an argument being constituted by correct inference rules will no more coincide. The gap between the two notions is accounted for by (...)
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  • Foundations of Intuitionistic Logic.G. Kreisel - 1965 - Journal of Symbolic Logic 30 (2):243-244.
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  • Identity of proofs based on normalization and generality.Kosta Došen - 2003 - Bulletin of Symbolic Logic 9 (4):477-503.
    Some thirty years ago, two proposals were made concerning criteria for identity of proofs. Prawitz proposed to analyze identity of proofs in terms of the equivalence relation based on reduction to normal form in natural deduction. Lambek worked on a normalization proposal analogous to Prawitz's, based on reduction to cut-free form in sequent systems, but he also suggested understanding identity of proofs in terms of an equivalence relation based on generality, two derivations having the same generality if after generalizing maximally (...)
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  • Proof and Paradox.Neil Tennant - 1982 - Dialectica 36 (2‐3):265-296.
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  • Basic logic: Reflection, symmetry, visibility.Giovanni Sambin, Giulia Battilotti & Claudia Faggian - 2000 - Journal of Symbolic Logic 65 (3):979-1013.
    We introduce a sequent calculus B for a new logic, named basic logic. The aim of basic logic is to find a structure in the space of logics. Classical, intuitionistic, quantum and non-modal linear logics, are all obtained as extensions in a uniform way and in a single framework. We isolate three properties, which characterize B positively: reflection, symmetry and visibility. A logical constant obeys to the principle of reflection if it is characterized semantically by an equation binding it with (...)
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  • Rules for subatomic derivation.Bartosz Więckowski - 2011 - Review of Symbolic Logic 4 (2):219-236.
    In proof-theoretic semantics the meaning of an atomic sentence is usually determined by a set of derivations in an atomic system which contain that sentence as a conclusion (see, in particular, Prawitz, 1971, 1973). The paper critically discusses this standard approach and suggests an alternative account which proceeds in terms of subatomic introduction and elimination rules for atomic sentences. A simple subatomic normal form theorem by which this account of the semantics of atomic sentences and the terms from which they (...)
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  • The Idea of a Proof-Theoretic Semantics and the Meaning of the Logical Operations.Heinrich Wansing - 2000 - Studia Logica 64 (1):3-20.
    This is a purely conceptual paper. It aims at presenting and putting into perspective the idea of a proof-theoretic semantics of the logical operations. The first section briefly surveys various semantic paradigms, and Section 2 focuses on one particular paradigm, namely the proof-theoretic semantics of the logical operations.
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  • What’s Wrong with Tonk.Roy T. Cook - 2005 - Journal of Philosophical Logic 34 (2):217 - 226.
    In “The Runabout Inference Ticket” AN Prior (1960) examines the idea that logical connectives can be given a meaning solely in virtue of the stipulation of a set of rules governing them, and thus that logical truth/consequence.
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  • Fitch's paradox of knowability.Michael Dummett - 2008 - In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford, England and New York, NY, USA: Oxford University Press.
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  • Classical logic without bivalence.Tor Sandqvist - 2009 - Analysis 69 (2):211-218.
    Semantic justifications of the classical rules of logical inference typically make use of a notion of bivalent truth, understood as a property guaranteed to attach to a sentence or its negation regardless of the prospects for speakers to determine it as so doing. For want of a convincing alternative account of classical logic, some philosophers suspicious of such recognition-transcending bivalence have seen no choice but to declare classical deduction unwarranted and settle for a weaker system; intuitionistic logic in particular, buttressed (...)
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  • Proof-theoretic validity.Stephen Read - 2015 - In Colin R. Caret & Ole T. Hjortland (eds.), Foundations of Logical Consequence. Oxford, England: Oxford University Press. pp. 136-158.
    The idea of proof-theoretic validity originated in the work of Gentzen, when he suggested that the meaning of each logical expression was encapsulated in its introduction-rules. The idea was developed by Prawitz and Dummett, but came under attack by Prior under the soubriquet 'analytic validity'. Logical truths and logical consequences are deemed analytically valid by virtue of following, in a way which the present chapter clarifies, from the meaning of the logical constants. But different logics are based on different rules, (...)
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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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  • On flattening elimination rules.Grigory K. Olkhovikov & Peter Schroeder-Heister - 2014 - Review of Symbolic Logic 7 (1):60-72.
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  • 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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