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Chapter 4 Kearns: Reading guide

Make sure you know what the following concepts mean and how to use them appropriately:

  • restricted quantifier
  • restrictor
  • relations between sets in set theory: identity (=), proper subset, subset, set difference (check book for missing symbols)
  • cardinality of a set (||)
  • operators for number comparison >, <, and related (check book for symbols)
  • strong and weak determiners, noun phrases
Make sure you understand:
  • that "in Generalized Quantifier Theory a quantifier determiner expresses a relation between sets" (Kearns, p. 73; my boldface)
  • that we give a semantics to the logical formulae we build through the use of set theory: in particular, 
    • we establish what the relationship between the set denoted by the restrictor and the set denoted by the predicate must be for the sentence to be true,
    • using relations between sets and comparisons between their cardinalities
  • the difference between strong and weak determiners wrt the role they play in discourse
Make sure you know how to:
  • translate a sentence with one or more restricted quantifier into a formula in predicate logic
  • represent the scopal ambiguity introduced by quantifiers using restricted quantifiers (see example (15))
    • AND paraphrase the different meanings represented by each formalization
  • express the truth conditions of a sentence involving restricted quantifiers using set theory
  • how to identify strong and weak determiners / noun phrases (section 4.5)