Scope as syntactic abstraction

Chris Barker

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    What is the logic of scope? By “scope”, I mean scopetaking in natural languages such as English, as illustrated by the sentence Ann saw everyone. In this example, the quantifier denoted by everyone takes scope over the rest of the sentence, that is, it takes the denotation of the rest of the sentence as its semantic argument: everyone(λx.saw(x)(ann)). The answer I will give here will be to provide a substructural logic whose two modes are related by a single structural postulate. This postulate can be interpreted as constituting a kind of lambda-abstraction over structures, where the abstracted structures are interpreted as delimited continuations. I discuss soundness and completeness results, as well as cut elimination. I also compare the logic to a number of alternative approaches, including the standard technique of Quantifier Raising, and mention applications to scope ambiguity and parasitic scope.

    Original languageEnglish (US)
    Title of host publicationNew Frontiers in Artificial Intelligence - JSAI-isAI 2014 Workshops, LENLS, JURISIN, and GABA, Revised Selected Papers
    EditorsTsuyoshi Murata, Koji Mineshima, Daisuke Bekki
    PublisherSpringer Verlag
    Pages184-199
    Number of pages16
    ISBN (Print)9783662481189
    DOIs
    StatePublished - Jan 1 2015
    Event6th International Symposium on Artificial Intelligence, JSAI 2014 - Kanagawa, Japan
    Duration: Oct 27 2014Oct 28 2014

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume9067
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other6th International Symposium on Artificial Intelligence, JSAI 2014
    CountryJapan
    CityKanagawa
    Period10/27/1410/28/14

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    Keywords

    • Continuations
    • Natural language quantification
    • Parasitic scope
    • Quantifier raising
    • Scope
    • Substructural logic

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Barker, C. (2015). Scope as syntactic abstraction. In T. Murata, K. Mineshima, & D. Bekki (Eds.), New Frontiers in Artificial Intelligence - JSAI-isAI 2014 Workshops, LENLS, JURISIN, and GABA, Revised Selected Papers (pp. 184-199). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9067). Springer Verlag. https://doi.org/10.1007/978-3-662-48119-6_14