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Higher-Order Syllogistics

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Book cover Formal Grammar (FG 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8612))

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Abstract

We propose a distinction between bottom-up and top-down systems of natural logic, with the classical syllogism epitomizing the first and the Monotonicity Calculus the second. We furthermore suggest it useful to view top-down systems as higher-order generalizations of broadly syllogistic systems. We illustrate this view by proving a result of independent interest: we axiomatize the first-order/single-type fragment of a higher-order calculus for reasoning about inclusion and exclusion (MacCartney and Manning, 2009; Icard, 2012). We show this logic is equivalent to a syllogistic logic with All and nominal complementation, in fact a fragment of a system recently studied (Moss, 2010b).

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Author information

Authors and Affiliations

  1. Department of Philosophy, Stanford University, California, USA

    Thomas F. Icard III

Authors
  1. Thomas F. Icard III
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Editors and Affiliations

  1. Departament de Llenguatges i Sistemes,Informàtics, Universitat Politècnica de Catalunya, Jordi Girona Salgado,1-3, 08034, Barcelona, Spain

    Glyn Morrill

  2. Department of Philosophy, Tilburg University, P.O. Box 90153, NL 5000, LE Tilburg, The Netherlands

    Reinhard Muskens

  3. Department of Linguistics and Information Science, Heinrich-Heine-University Düsseldorf, Universitätsstrasse 1, 40225, Düsseldorf, Germany

    Rainer Osswald

  4. Institute for English and American Studies, Department of Linguistic, Goethe University Frankfurt am Main, Grüneburgplatz 1, 60323, Frankfurt, Germany

    Frank Richter

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Icard, T.F. (2014). Higher-Order Syllogistics. In: Morrill, G., Muskens, R., Osswald, R., Richter, F. (eds) Formal Grammar. FG 2014. Lecture Notes in Computer Science, vol 8612. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44121-3_1

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  • DOI: https://doi.org/10.1007/978-3-662-44121-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44120-6

  • Online ISBN: 978-3-662-44121-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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