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3 results

Higher-Order Logic and Type Theory

Higher-Order Logic and Type Theory
  • John L. Bell
  • Published online:
    10 March 2022
    Print publication:
    31 March 2022
  • This Element is an exposition of second- and higher-order logic and type theory. It begins with a presentation of the syntax and semantics of classical second-order logic, pointing up the contrasts with first-order logic. This leads to a discussion of higher-order logic based on the concept of a type. The second Section contains an account of the origins and nature of type theory, and its relationship to set theory. Section 3 introduces Local Set Theory (also known as higher-order intuitionistic logic), an important form of type theory based on intuitionistic logic. In Section 4 number of contemporary forms of type theory are described, all of which are based on the so-called 'doctrine of propositions as types'. We conclude with an Appendix in which the semantics for Local Set Theory - based on category theory - is outlined.

  • 13 - Comparatives and Superlatives

  • Rodney Huddleston, University of Queensland, Geoffrey K. Pullum, University of Edinburgh, Brett Reynolds
  • Book:
    A Student's Introduction to English Grammar
    Published online:
    20 January 2022
    Print publication:
    25 November 2021, pp 297-310

  • Summary

    Comparison involves morphology and syntax for describing something as ranking above or below something else, as being equivalent to something, or as falling at the very top or the very bottom of the scale. Many adjectives do this by inflecting for grade, having plain, comparative and superlative forms. This inflectional system applies also to a small number of determinatives and adverbs. Others are modified by ‘more’ or ‘less’.

    Superlatives express set comparison, with one item outranking all of the others. The comparative form, by contrast, is predominantly used in term comparison – comparison between a primary term and a secondary term. There are also comparisons of equality, which are always marked by a modifying phrase rather than by inflection, along with a type of non-scalar comparison where the issue is simply of identity or similarity.

    The prepositions ‘than’ and ‘as’ often license as complements a distinctive type of subordinate clause called a comparative clause. Comparative clauses constitute one of the three major kinds of tensed subordinate clause, being distinctive in that they are obligatorily reduced in certain ways relative to the structure of main clauses.

  • Measuring the Impact of Externalities on College of Agriculture Teaching Evaluations

  • Ronald A. Fleming, Ernest F. Bazen, Michael E. Wetzstein
  • Journal:
    Journal of Agricultural and Applied Economics / Volume 37 / Issue 3 / December 2005
    Published online by Cambridge University Press:
    28 April 2015, pp. 635-645

  • Student evaluation of teaching (SET) is employed as an aid in improving instruction and determining faculty teaching effectiveness. However, economic theory indicates the existence of externalities in SET scores that directly influence their interpretation. As a test of this existence, a multinomial-choice, ordered data estimation procedure is employed to identify course externalities influencing SET. These externalities include student class standing, required courses, class size, days a class meets, class meeting time, classroom location, and classroom design. Results indicate that externalities have a significant impact on teaching evaluations. Thus, failure to internalize these externalities will lead to biases in SET and questionable use of SET as an aid in instruction improvement and determining faculty effectiveness.