Universal Quantification

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Universal quantification is quantification with the quantifier #$forAll. In CycL formulas, variables which are not explicitly bound by a quantifier are assumed to be universally quantified. For example,

(forAll ?LEAF (implies
    (isa ?LEAF Leaf)
    (colorOfObject ?LEAF GreenColor)))

means that every leaf is green. But in CycL — wherein universal quantification is implicit for any apparently “open” variables in an assertion — the sentence above means the same as the following sentence:

(implies
  (isa ?LEAF Leaf)
  (colorOfObject ?LEAF GreenColor))

See also

  • Existential quantification

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