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What is higher order logic?

  • A.A logic permitting quantification over predicates and functions
  • B.A logic with more than two truth values available
  • C.A logic in which formulas may be nested arbitrarily deeply
  • D.A logic that reasons about the properties of other logics

Answer: A

Higher order logic quantifies over relations as well as objects, so a statement such as there is a property shared by these two things becomes expressible. It is far more expressive and has no complete proof procedure, so most work stays first order and encodes what it can. Truth values, nesting and metatheory are different notions. Each step up in what may be quantified over buys expressiveness and costs a metatheoretical guarantee, which is the same trade seen throughout.

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