quantifier

n. word that expresses a quantity (Grammar)

The term quantification has several meanings, general and specific. Primarily it covers all those acts which quantify observations and experiences by converting them into numbers through counting and measuring. It is thus the basis for mathematics and for science.Some measure of the undisputed general importance of quantification in the natural sciences can be gleaned from the following comments: these are mere facts, but they are quantitative facts and the basis of science. It seems to be held as universally true that the foundation of quantification is measurement. There is little doubt that quantification provided a basis for the objectivity of science. In ancient times, musicians and artists...rejected quantification, but merchants, by definition, quantified their affairs, in order to survive, made them visible on parchment and paper. Any reasonable comparison between Aristotle and Galileo shows clearly that there can be no unique lawfulness discovered without detailed quantification. Even today, universities use imperfect instruments called 'exams' to indirectly quantify something they call knowledge.
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Noun
1. (logic) a word (such as `some' or `all' or `no') that binds the variables in a logical proposition
(synonym) logical quantifier
(hypernym) word
(hyponym) existential quantifier, existential operator
(classification) logic
2. (grammar) a word that expresses a quantity (as `fifteen' or `many')
(hypernym) word
(hyponym) universal quantifier
(classification) grammar

v. quantify, determine quantity; express the quantity

<logic> An operator in predicate logic specifying for which values of a variable a formula is true. Universally quantified means "for all values" (written with an inverted A, LaTeX \forall) and existentially quantified means "there exists some value" (written with a reversed E, LaTeX \exists). To be unambiguous, the set to which the values of the variable belong should be specified, though this is often omitted when it is clear from the context (the "universe of discourse"). E.g.
Forall x . P(x) not (Exists x . not P(x))
meaning that any x (in some unspecified set) has property P which is equivalent to saying that there does not exist any x which does not have the property.
If a variable is not quantified then it is a free variable. In logic programming this usually means that it is actually universally quantified.
See also first order logic.
(2002-05-21)