Higher-Order Syllogistics

  • Thomas F. IcardIII
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8612)


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).


syllogistics natural logic exclusion surface reasoning 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Thomas F. IcardIII
    • 1
  1. 1.Department of PhilosophyStanford UniversityUSA

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