Quantification

In language and logic, quantification is a construct that specifies the extent of validity of a predicate, that is the extent to which a predicate holds over a range of things. A language element which generates a quantification is called a quantifier. The resulting statement is a quantified statement, and we say we have quantified over the predicate. Quantification is used in both natural languages and formal languages. In natural language, examples of quantifiers are for all, for some; many, few, a lot are also quantifiers. 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 as an extent of validity. Quantification is an example of a variable-binding operation.

Related Topics:
Language - Logic - Natural language - Formal language - Semantics - Variable-binding operation

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The two fundamental kinds of quantification in predicate logic are universal quantification and existential quantification. These concepts are covered in detail in their individual articles; here we discuss features of quantification that apply in both cases.

Related Topics:
Predicate logic - Universal quantification - Existential quantification

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Other kinds of quantification include uniqueness quantification.

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