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A Framework for the Hyperintensional Semantics of Natural Language with Two Implementations

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Logical Aspects of Computational Linguistics (LACL 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2099))

Abstract

In this paper we present a framework for constructing hyperintensional semantics for natural language. On this approach, the axiom of extensionality is discarded from the axiom base of a logic. Weaker conditions are specified for the connection between equivalence and identity which prevent the reduction of the former relation to the latter. In addition, by axiomatising an intensional number theory we can provide an internal account of proportional cardinality quantifiers, like most. We use a (pre-)lattice defined in terms of a (pre-)order that models the entailment relation. Possible worlds/situations/indices are then prime filters of propositions in the (pre-)lattice. Truth in a world/situation is then reducible to membership of a prime filter. We showho wthi s approach can be implemented within (i) an intensional higher-order type theory, and (ii) first-order property theory.

Abstract

We are grateful to Tom Maibaum and Carl Pollard for invaluable help and advice in developing the semantic approach proposed here. Much of the the second author’s research relies heavily on earlier joint work with Pollard, and we are grateful to him for helpful comments on an earlier draft of this paper. We would also like to thank Nissim Francez, Dov Gabbay, Jonathan Ginzburg, Howard Gregory, Jim Lambek, AndrewPit ts, Phil Scott and three anonymous referees for useful discussion of many of the ideas presented in this paper. Of course we bear sole responsibility for the shortcomings of our proposals. The second author’s research is funded by grant number AN2687/APN 9387 from the Arts and Humanities Research Board of the United Kingdom.

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Authors and Affiliations

  1. Dept. of Computer Science, King’s College London, The Strand, London, WC2R 2LS, UK

    Chris Fox & Shalom Lappin

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  1. Chris Fox
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  2. Shalom Lappin
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Editors and Affiliations

  1. INRIA Lorraine, 615 rue du Jardin Botanique, B.P. 101, 54602, Villers-lès-Nancy Cedex, France

    Philippe de Groote

  2. Universitat Politècnica de Catalunya, Jordi Girona Salgado, 1-3, 08028, Barcelona, Spain

    Glyn Morrill

  3. Faculté des Sciences, Institut de recherche en Informatique de Nantes (IRIN), 2, rue de la Houssinière, B.P. 92208, 44322, Nantes Cedex 03, France

    Christian Retoré

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Fox, C., Lappin, S. (2001). A Framework for the Hyperintensional Semantics of Natural Language with Two Implementations. In: de Groote, P., Morrill, G., Retoré, C. (eds) Logical Aspects of Computational Linguistics. LACL 2001. Lecture Notes in Computer Science(), vol 2099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48199-0_11

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  • DOI: https://doi.org/10.1007/3-540-48199-0_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42273-0

  • Online ISBN: 978-3-540-48199-7

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