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A proof-theoretic approach to scope ambiguity in compositional vector space models

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EN
Abstrakty
EN
We investigate the extent to which compositional vector space models can be used to account for scope ambiguity in quantified sentences (of the form Every man loves some woman). Such sentences containing two quantifiers introduce two readings, a direct scope reading and an inverse scope reading. This ambiguity has been treated in a vector space model using bialgebras by Hedges and Sadrzadeh (2016) and Sadrzadeh (2016), though without an explanation of the mechanism by which the ambiguity arises. We combine a polarised focussed sequent calculus for the non-associative Lambek calculus NL, as described in Moortgat and Moot (2011), with the vector-based approach to quantifier scope ambiguity. In particular, we establish a procedure for obtaining a vector space model for quantifier scope ambiguity in a derivational way.
Rocznik
Strony
261--286
Opis fizyczny
Bibliogr. 25 poz., rys., tab.
Twórcy
  • School of Electronic Engineering and Computer Science, Queen Mary University of London
Bibliografia
  • [1] Jean-Marc Andreoli (2001), Focussing and proof construction, Annals of Pure and Applied Logic, 107 (1):131-163, doi: https://doi.org/10.1016/S0168-0072(00)00032-4.
  • [2] Arno Bastenhof (2012), Polarized Montagovian semantics for the Lambek-Grishin calculus, in Philippe de Groote and Mark-Jan Nederhof, editors, 15th and 16th International Conference on Formal Grammar, volume 7395, pp. 1-16, Springer, Springer-Verlag Berlin Heidelberg, doi: http://dx.doi.org/10.1007/978-3-642-32024-8.
  • [3] Raffaella Bernardi and Michael Moortgat (2010), Continuation semantics for the Lambek-Grishin calculus, Information and Computation, 208 (5):397-416, doi: https://doi.org/10.1016/j.ic.2009.11.005.
  • [4] Bob Coecke, Edward Grefenstette, and Mehrnoosh Sadrzadeh (2013), Lambek vs. Lambek: Functorial vector space semantics and string diagrams for Lambek calculus, Annals of Pure and Applied Logic, 164 (11):1079-1100, doi: https://doi.org/10.1016/j.apal.2013.05.009.
  • [5] Bob Coecke, Mehrnoosh Sadrzadeh, and Stephen Clark (2010), Mathematical foundations for a compositional distributional model of meaning, arXiv preprint arXiv:1003.4394, https://arxiv.org/pdf/1003.4394.
  • [6] Matej Dostal and Mehrnoosh Sadrzadeh (2016), Many valued generalised quantifiers for natural language in the DisCoCat model, Technical report, Czech Technical University Prague and Queen Mary University of London, https://qmro.qmul.ac.uk/xmlui/bitstream/handle/123456789/17382/DisCoCat%20Maodel%20Paper%20M.Sadrzadeh.pdf.
  • [7] Edward Grefenstette (2013), Towards a formal distributional semantics: simulating logical calculi with tensors, in Proceedings of the Second Joint Conference on Lexical and Computational Semantics, pp. 1-10, Association for Computational Linguistics, http://aclweb.org/anthology/S13-1001.
  • [8] Jules Hedges and Mehrnoosh Sadrzadeh (2016), A generalised quantifier theory of natural language in categorical compositional distributional semantics with bialgebras, arXiv preprint arXiv:1602.01635, https://arxiv.org/pdf/1602.01635.
  • [9] Dimitri Kartsaklis (2016), Coordination in categorical compositional distributional semantics, arXiv preprint arXiv:1606.01515, https://arxiv.org/pdf/1606.01515.
  • [10] Dimitri Kartsaklis, Matthew Purver, and Mehrnoosh Sadrzadeh (2016), Verb phrase ellipsis using Frobenius algebras in categorical compositional distributional semantics, DSALT Workshop, European Summer School on Logic, Language and Information, https://pdfs.semanticscholar.org/6c56/137ffb008ee5f94a482e0c74e494d7f7bc04.pdf.
  • [11] Germán Kruszewski, Denis Paperno, Raffaella Bernardi, and Marco Baroni (2016), There is no logical negation here, but there are alternatives: Modeling conversational negation with distributional semantics, Computational Linguistics, 42 (4):637-660, doi: https://doi.org/10.1162/COLI_a_00262.
  • [12] Joachim Lambek (1958), The mathematics of sentence structure, The American Mathematical Monthly, 65 (3):154-170, doi: https://doi.org/10.1080/00029890.1958.11989160.
  • [13] Joachim Lambek (1997), Type grammar revisited, in International Conference on Logical Aspects of Computational Linguistics, pp. 1-27, Springer, doi: https://doi.org/10.1007/3-540-48975-4_1.
  • [14] Richard Montague (1970), English as a formal language, Linguaggi nella Società e nella Tecnica.
  • [15] Richard Montague (1973), The proper treatment of quantification in ordinary English, in Approaches to Natural Language, pp. 221-242, Springer, doi: https://doi.org/10.1007/978-94-010-2506-5_10.
  • [16] Michael Moortgat and Richard Moot (2011), Proof nets for the Lambek-Grishin calculus, arXiv preprint arXiv:1112.6384, https://arxiv.org/pdf/1112.6384.
  • [17] Michael Moortgat and Gijs Wijnholds (2017), Lexical and derivational meaning in vector-based models of relativisation, Proceedings of the 21st Amsterdam Colloquium, pp. 55-64, https://semanticsarchive.net/Archive/jZiM2FhZ/AC2017-Proceedings.pdf.
  • [18] Glyn Morrill, Oriol Valentín, and Mario Fadda (2011), The displacement calculus, Journal of Logic, Language and Information, 20 (1):1-48, doi: https://doi.org/10.1007/s10849-010-9129-2.
  • [19] Mehrnoosh Sadrzadeh (2016), Quantifier scope in categorical compositional distributional semantics, arXiv preprint arXiv:1608.01404, https://arxiv.org/pdf/1608.01404.
  • [20] Mehrnoosh Sadrzadeh, Stephen Clark, and Bob Coecke (2013), The Frobenius anatomy of word meanings I: subject and object relative pronouns, Journal of Logic and Computation, 23 (6):1293-1317, doi: https://doi.org/10.1093/logcom/ext044.
  • [21] Mark Steedman (2000), The Syntactic Process, MIT Press.
  • [22] Oriol Valentín (2014), The hidden structural rules of the discontinuous Lambek calculus, in Categories and Types in Logic, Language, and Physics, pp. 402-420, Springer, doi: https://doi.org/10.1007/978-3-642-54789-8_23.
  • [23] Gijs Wijnholds (2014), Categorical foundations for extended compositional distributional models of meaning, Master’s thesis, Universiteit van Amsterdam, https://www.illc.uva.nl/Research/Publications/Reports/reportlist/MoL-2014-22.text.pdf.
  • [24] Gijs Jasper Wijnholds (2017), Coherent diagrammatic reasoning in compositional distributional semantics, in International Workshop on Logic, Language, Information, and Computation, pp. 371-386, Springer, doi: https://doi.org/10.1007/978-3-662-55386-2_27.
  • [25] Lotfi A. Zadeh (1983), A computational approach to fuzzy quantifiers in natural languages, Computers & Mathematics with Applications, 9 (1):149-184, ISSN 0898-1221, doi: http://dx.doi.org/10.1016/0898-1221(83)90013-5.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
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Bibliografia
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bwmeta1.element.baztech-d6957eea-4c1a-449d-a6f0-2837f4d41fc0
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