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  1. Proof-theoretic semantic values for logical operators.Nissim Francez & Gilad Ben-avi - 2011 - Review of Symbolic Logic 4 (3):466-478.
    The paper proposes a semantic value for the logical constants (connectives and quantifiers) within the framework of proof-theoretic semantics, basic meaning on the introduction rules of a meaning conferring natural deduction proof system. The semantic value is defined based on Fregecontributions” to sentential meanings as determined by the function-argument structure as induced by a type-logical grammar. In doing so, the paper proposes a novel proof-theoretic interpretation of the semantic types, traditionally interpreted in Henkin models. The compositionality of the resulting attribution (...)
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  • A Note on Harmony.Nissim Francez & Roy Dyckhoff - 2012 - Journal of Philosophical Logic 41 (3):613-628.
    In the proof-theoretic semantics approach to meaning, harmony , requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony , requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony : imposes the existence of certain transformations of derivations, known as reduction and expansion . We propose (...)
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  • Tonk, Plonk and Plink.Nuel Belnap - 1962 - Analysis 22 (6):130-134.
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  • (1 other version)The proper treatment of quantification in ordinary English.Richard Montague - 1973 - In Patrick Suppes, Julius Moravcsik & Jaakko Hintikka (eds.), Approaches to Natural Language. Dordrecht. pp. 221--242.
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  • (1 other version)The runabout inference ticket.Arthur Prior - 1967 - In Peter Frederick Strawson (ed.), Philosophical logic. London,: Oxford University Press. pp. 38-9.
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  • The grammar of intentionality.Richard Larson - 2002 - In Gerhard Preyer & Georg Peter (eds.), Logical Form and Language. Oxford, England: Oxford University Press. pp. 228--62.
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  • Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
    This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.
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  • Articulating reasons: an introduction to inferentialism.Robert Brandom - 2000 - Cambridge: Harvard University Press.
    This new work provides an approachable introduction to the complex system that Making It Explicit mapped out.
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  • The handbook of contemporary semantic theory.Shalom Lappin (ed.) - 1996 - Cambridge, Mass., USA: Blackwell Reference.
    1. Formal semantics in linguistics -- 2. Generalized quantifier theory -- 3. The interface between syntax and semantics -- 4. Anaphora, discourse, and modality -- 5. Focus, presupposition, and negation -- 6. Tense -- 7. Questions -- 8. Plurals -- 9. Computational semantics -- 10. Lexical semantics -- 11. Semantics and related domains.
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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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  • (1 other version)Generalized quantifiers and natural language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
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  • Ontological Relativity and Other Essays.Willard Van Orman Quine - 1969 - New York: Columbia University Press.
    This volume consists of the first of the John Dewey Lectures delivered under the auspices of Columbia University's Philosophy Department as well as other essays by the author. Intended to clarify the meaning of the philosophical doctrines propounded by Professor Quine in 'Word and Objects', the essays included herein both support and expand those doctrines.
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  • Categorial Type Logics.Michael Moortgat - 1997 - In J. F. A. K. Van Benthem, Johan van Benthem & Alice G. B. Ter Meulen (eds.), Handbook of Logic and Language. Elsevier.
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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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  • Type-theoretical Grammar.Aarne Ranta - 1994 - Oxford, England: Oxford University Press on Demand.
    It is the aim of INDICES to document recent explorations in the various fields of philosophical logic and formal linguistics and their applications in other disciplines. The main emphasis of this series is on self-contained monographs covering particular areas of recent research and surveys of methods, problems, and results in all fields of inquiry where recourse to logical analysis and logical methods has been fruitful. INDICES will contain monographs dealing with the central areas of philosophical logic (extensional and intensional systems, (...)
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  • Investigations into Logical Deduction.Gerhard Gentzen - 1964 - American Philosophical Quarterly 1 (4):288 - 306.
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  • On the proper treatment of opacity in certain verbs.Thomas Ede Zimmermann - 1993 - Natural Language Semantics 2 (1):149-179.
    This paper is about the semantic analysis of referentially opaque verbs like seek and owe that give rise to nonspecific readings. It is argued that Montague's categorization (based on earlier work by Quine) of opaque verbs as properties of quantifiers runs into two serious difficulties: the first problem is that it does not work with opaque verbs like resemble that resist any lexical decomposition of the seek ap try to find kind; the second one is that it wrongly predicts de (...)
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  • Anti-realism and logic: truth as eternal.Neil Tennant - 1987 - New York: Oxford University Press.
    Anti-realism is a doctrine about logic, language, and meaning that is based on the work of Wittgenstein and Frege. In this book, Professor Tennant clarifies and develops Dummett's arguments for anti-realism and ultimately advocates a radical reform of our logical practices.
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  • Anti-realist semantics.Wolfram Hinzen - 2000 - Erkenntnis 52 (3):281-311.
    I argue that the implementation of theDummettian program of an ``anti-realist'' semanticsrequires quite different conceptions of the technicalmeaning-theoretic terms used than those presupposed byDummett. Starting from obvious incoherences in anattempt to conceive truth conditions as assertibilityconditions, I argue that for anti-realist purposesnon-epistemic semantic notions are more usefully kept apart from epistemic ones rather than beingreduced to them. Embedding an anti-realist theory ofmeaning in Martin-Löf's Intuitionistic Type Theory(ITT) takes care, however, of many notorious problemsthat have arisen in trying to specify suitableintuitionistic (...)
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  • (1 other version)The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38-39.
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  • Natural deduction with general elimination rules.Jan von Plato - 2001 - Archive for Mathematical Logic 40 (7):541-567.
    The structure of derivations in natural deduction is analyzed through isomorphism with a suitable sequent calculus, with twelve hidden convertibilities revealed in usual natural deduction. A general formulation of conjunction and implication elimination rules is given, analogous to disjunction elimination. Normalization through permutative conversions now applies in all cases. Derivations in normal form have all major premisses of elimination rules as assumptions. Conversion in any order terminates.Through the condition that in a cut-free derivation of the sequent Γ⇒C, no inactive weakening (...)
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  • Proof theory and meaning: The context of deducibility.Greg Restall - 2010 - In Françoise Delon, Ulrich Kohlenbach, Penelope Maddy & Frank Stephan (eds.), Logic Colloquium 2007. New York: Cambridge University Press. pp. 204-219.
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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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  • Intensional verbs and quantifiers.Friederike Moltmann - 1997 - Natural Language Semantics 5 (1):1-52.
    This paper discusses the semantics of intensional transitive verbs such as 'need', 'want','recognize', 'find', and 'hire'. It proposes new linguistic criteria for intensionality and defends two semantic analyses for two different classes of intensional verbs. The paper also includes a systematic classification of intensional verbs according to the type of lexical meaning they involve.
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  • Conservative generalized quantifiers and presupposition.Tim Fernando - manuscript
    Conservativity in generalized quantifiers is linked to presupposition filtering, under a propositions-as-types analysis extended with dependent quantifiers. That analysis is underpinned by modeltheoretically interpretable proofs which inhabit propositions they prove, thereby providing objects for quantification and hooks for anaphora.
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  • Whose challenge? Which semantics?Stephen Boulter - 2001 - Synthese 126 (1-2):325 - 337.
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  • Seeking a centaur, adoring adonis: Intensional transitives and empty terms.Mark Richard - 2001 - Midwest Studies in Philosophy 25 (1):103–127.
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  • Identity and harmony.Stephen Read - 2004 - Analysis 64 (2):113-119.
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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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  • Absolute generality.Agustín Rayo & Gabriel Uzquiano (eds.) - 2006 - New York: Oxford University Press.
    The problem of absolute generality has attracted much attention in recent philosophy. Agustin Rayo and Gabriel Uzquiano have assembled a distinguished team of contributors to write new essays on the topic. They investigate the question of whether it is possible to attain absolute generality in thought and language and the ramifications of this question in the philosophy of logic and mathematics.
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  • Monotonicity in opaque verbs.Thomas Ede Zimmermann - 2006 - Linguistics and Philosophy 29 (6):715 - 761.
    The paper is about the interpretation of opaque verbs like “seek”, “owe”, and “resemble” which allow for unspecific readings of their (indefinite) objects. It is shown that the following two observations create a problem for semantic analysis: (a) The opaque position is upward monotone: “John seeks a unicorn” implies “John seeks an animal”, given that “unicorn” is more specific than “animal”. (b) Indefinite objects of opaque verbs allow for higher-order, or “underspecific”, readings: “Jones is looking for something Smith is looking (...)
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  • (1 other version)Intuitionistic Logic.Dirk van Dalen - 2002 - In D. M. Gabbay & F. Guenthner (eds.), ¸ Itegabbay2002. Kluwer Academic Publishers. pp. 1-115.
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  • Language and its Models: Is Model Theory a Theory of Semantics?Jaroslav Peregrin - 1997 - Nordic Journal of Philosophical Logic 2 (1):1-23.
    Tarskian model theory is almost universally understood as a formal counterpart of the preformal notion of semantics, of the “linkage between words and things”. The wide-spread opinion is that to account for the semantics of natural language is to furnish its settheoretic interpretation in a suitable model structure; as exemplified by Montague 1974.
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  • Intensional verbs and their intentional objects.Friederike Moltmann - 2008 - Natural Language Semantics 16 (3):239-270.
    The complement of intensional transitive verbs, like any nonreferential complement, can be replaced by a ‘special quantifier’ or ‘special pronoun’ such as 'something', 'the same thing', or 'what'. In this paper, I will defend the ‘Nominalization Theory’ of special quantifiers against a range of apparent counterexamples involving intensional transitive verbs.
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  • Natural deduction rules for English.Frederic B. Fitch - 1973 - Philosophical Studies 24 (2):89 - 104.
    A system of natural deduction rules is proposed for an idealized form of English. The rules presuppose a sharp distinction between proper names and such expressions as the c, a (an) c, some c, any c, and every c, where c represents a common noun. These latter expressions are called quantifiers, and other expressions of the form that c or that c itself, are called quantified terms. Introduction and elimination rules are presented for any, every, some, a (an), and the, (...)
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  • (1 other version)Generalized Quantifiers and Natural Language.Jon Barwise - 1980 - Linguistics and Philosophy 4:159.
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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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  • Robert B. Brandom, Articulating Reasons (An Introduction to Inferentialism). [REVIEW]Robert B. Brandom - 2001 - Erkenntnis 55 (1):121-127.
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