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Proof-theoretic semantic values for logical operators

Nissim Francez & Gilad Ben-avi

Review of Symbolic Logic 4 (3):466-478 (2011)

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Proof-Theoretic Semantics for Subsentential Phrases.Nissim Francez, Roy Dyckhoff & Gilad Ben-Avi - 2010 - Studia Logica 94 (3):381-401.details 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 (...) Download Export citation Bookmark 24 citations
Grundlagen der Arithmetik: Studienausgabe mit dem Text der Centenarausgabe.Gottlob Frege - 1884 - Breslau: Wilhelm Koebner Verlag.details Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister. Download Export citation Bookmark 309 citations
Rules for subatomic derivation.Bartosz Więckowski - 2011 - Review of Symbolic Logic 4 (2):219-236.details 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 (...) Download Export citation Bookmark 22 citations
Formal features of compositionality.Wilfrid Hodges - 2001 - Journal of Logic, Language and Information 10 (1):7-28.details We consider two formalisations of the notion of a compositionalsemantics for a language, and find some equivalent statements in termsof substitutions. We prove a theorem stating necessary and sufficientconditions for the existence of a canonical compositional semanticsextending a given partial semantics, after discussing what features onewould want such an extension to have. The theorem involves someassumptions about semantical categories in the spirit of Husserl andTarski. Download Export citation Bookmark 59 citations
Compositionality, Understanding, and Proofs.Peter Pagin - 2009 - Mind 118 (471):713 - 737.details The principle of semantic compositionality, as Jerry Fodor and Ernie Lepore have emphasized, imposes constraints on theories of meaning that it is hard to meet with psychological or epistemic accounts. Here, I argue that this general tendency is exemplified in Michael Dummett's account of meaning. On that account, the so-called manifestability requirement has the effect that the speaker who understands a sentence s must be able to tell whether or not s satisfies central semantic conditions. This requirement is not met (...) Download Export citation Bookmark 8 citations

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