Quantifier

Quantifier may refer to:

See also

Quantifier (logic)

In logic, quantification is a construct that specifies the quantity of specimens in the domain of discourse that satisfy an open formula. For example, in arithmetic, it allows the expression of the statement that every natural number has a successor. A language element which generates a quantification (such as "every") is called a quantifier. The resulting expression is a quantified expression, it is said to be quantified over the predicate (such as "the natural number x has a successor") whose free variable is bound by the quantifier. In formal languages, quantification is a formula constructor that produces new formulas from old ones. The semantics of the language specifies how the constructor is interpreted. Two fundamental kinds of quantification in predicate logic are universal quantification and existential quantification. The traditional symbol for the universal quantifier "all" is "∀", a rotated letter "A", and for the existential quantifier "exists" is "∃", a rotated letter "E". These quantifiers have been generalized beginning with the work of Mostowski and Lindström.

Quantifier (linguistics)

In linguistics and grammar, a quantifier is a type of determiner, such as all, some, many, few, a lot, and no, (but not numerals) that indicates quantity.

Quantification is also used in logic, where it is a formula constructor that produces new formulas from old ones. Natural languages' determiners have been argued to correspond to logical quantifiers at the semantic level.

Introduction

All known human languages make use of quantification (Wiese 2004). For example, in English:

The words in italics are quantifiers. There exists no simple way of reformulating any one of these expressions as a conjunction or disjunction of sentences, each a simple predicate of an individual such as That wine glass was chipped. These examples also suggest that the construction of quantified expressions in natural language can be syntactically very complicated. Fortunately, for mathematical assertions, the quantification process is syntactically more straightforward.