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Tytuł artykułu

A proof-theoretic semantics for contextual domain restriction

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Języki publikacji
EN
Abstrakty
EN
The paper presents a proof-theoretic semantics account of contextual domain restriction for quantified sentences in a fragment of English. First, the technique is exemplified in the more familiar first-order logic, and in its restricted quantification variant. Then, a proof-theoretic semantics for the NL fragment is reviewed, and extended to handling contextual domain restriction. The paper addresses both the descriptive facet of the problem, deriving meaning relative to a context, as well as the fundamental aspect, defining explicitly a context (suitable for quantifier domain restriction), and specifying what it is about such a context that brings about the variation of meaning due to it. The paper argues for the following principle (the context incorporation principle, CIP): for every quantified sentence S depending on a context c, there exists a sentence S′, the meaning of which is independent of c, s.t. the contextually restricted meaning of S is equal to the meaning of S′. Thus, the effect of a context can always be internalized. The current model-theoretic accounts of contextual domain restriction do not satisfy CIP, in that they imply intersection of some extension with an arbitrary subset of the domain, that need not be the denotation of any NL-expression.
Rocznik
Strony
249--283
Opis fizyczny
Bibliogr. 27 poz., rys.
Twórcy
autor
  • Computer Science Department, The Technion-IIT, Haifa, Israel
Bibliografia
  • [1] Hanoch Ben-Yami (2006), A critique of Frege on common nouns, Ratio, 19 (2): 148-155.
  • [2] Robert B. Brandom (2000), Articulating reasons, Harvard University Press, Cambridge, MA.
  • [3] Michael Dummett (1993), The logical basis of metaphysics, Harvard University Press, Cambridge, MA, USA, hard copy 1991.
  • [4] Nissim Francez (2014a), The granularity of meaning in proof-theoretic semantics, in Nicholas Asher and Sergei Soloview, editors, Proceedings of the 8th International Conference on Logical Aspects of Computational Linguistics (LACL), Toulouse, France, June 2014, volume 8535 of LNCS, pp. 96-106, Springer Verlag, Berlin/Heidelberg, Germany.
  • [5] Nissim Francez (2014b), A logic inspired by natural language: quantifiers as subnectors, Journal of Philosophical Logic, doi: 10.1007/s10992-014-9312-z.
  • [6] Nissim Francez (2014c), Views of proof-theoretic semantics: Reified proof-theoretic meanings, Journal of Computational Logic, special issue in honour of Roy Dyckhoff, doi: 10.1093/logcom/exu035.
  • [7] Nissim Francez and Gilad Ben-Avi (2011), Proof-theoretic semantic values for logical operators, Review of Symbolic Logic, 4 (3): 337-485.
  • [8] Nissim Francez and Gilad Ben-Avi (2014), A proof-theoretic reconstruction of generalized quantifiers, Journal of Semantics, doi: 10.1093/jos/ffu001.
  • [9] Nissim Francez and Roy Dyckhoff (2010), Proof-theoretic semantics for a natural language fragment, Linguistics and Philosophy, 33 (6): 447-477.
  • [10] Nissim Francez and Roy Dyckhoff (2012), A note on harmony, Journal of Philosophical Logic, 41 (3): 613-628.
  • [11] Nissim Francez, Roy Dyckhoff, and Gilad Ben-Avi (2010), Proof-theoretic semantics for subsentential phrases, Studia Logica 94, pp. 381-401.
  • [12] Nissim Francez and Bartosz Wieckowski (2014), A proof-theoretic semantics for contextual definiteness, in Enrico Moriconi and Laura Tesconi, editors, Second Pisa Colloquium in Logic, Language and Epistemology, ETS, Pisa, Italy.
  • [13] Gottlob Frege (1884), Die Grundlagen der Arithmetik [The basic laws of arithmetics], Georg Olms, Hildesheim, Germany.
  • [14] Gerhard Gentzen (1969), Investigations into logical deduction, in M. E. Szabo, editor, The collected papers of Gerhard Gentzen, pp. 68-131, North-Holland, Amsterdam, Netherlands, English translation of the 1935 paper in German.
  • [15] Michael Glanzberg (2006), Context and unrestricted quantification, in Augustìne Rayo and Gabriel Uzquiano, editors, Absolute Generality, Clarendon Press, Oxford, UK.
  • [16] Michael Moortgat (1997), Categorial type logics, in Johan van Benthem and Alice ter Meulen, editors, Handbook of Logic and Language, pp. 93-178, North-Holland, Amsterdam, Netherlands.
  • [17] Lawrence Moss (2010), Syllogistic logics with verbs, Journal of Logic and Computation, 20 (4): 947-967.
  • [18] Francis Jeffrey Pelletier (2003), Context dependence and compositionality, Mind & Language, 18 (2): 148-161.
  • [19] Dag Prawitz (1965), Natural deduction: A proof-theoretical study, Almqvist and Wicksell, Stockholm, Sweden, soft cover edition by Dover, 2006.
  • [20] Dag Prawitz (2006), Meaning approached via proofs, Synthese, 148: 507-524.
  • [21] Arthur N. Prior (1960), The runabout inference-ticket, Analysis, 21: 38-39.
  • [22] Peter Schroeder-Heister (1984), A natural extension of natural deduction, Journal of Symbolic Logic, 49: 1284-1300.
  • [23] Jason Stanley and Zoltán Gendler Szabó (2000), On quantifier domain restriction, Mind & Language, 2-3: 219-261.
  • [24] Neil Tennant (1997), The taming of the true, Oxford University Press, Oxford, UK.
  • [25] Jan von Plato (2000), A problem with normal form in natural deduction, Mathematical Logic Quarterly, 46: 121-124.
  • [26] Jan von Plato (2001), Natural deduction with general elimination rules, Archive for Mathematical Logic, 40: 541-567.
  • [27] Dag Westerståhl (1985), Determiners and context sets, in Johan van Benthem and Alice ter Meulen, editors, Generalized Quantifiers in Natural Language, Foris, Dordrecht, Netherlands.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
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