Quantification Topics

• existential quantification
• language element
• principles of mathematics
• formal languages
• bertrand russell
• contraposition
• natural languages
• free variable
• quantifier
• quantifiers
• dimple
• predicate
• natural language
• arithmetic
• straight line
• constructor
• uniqueness
• discourse
• expression
• logic

Related Images

Source

del.icio.us Tags

• math
• wikipedia
• discrete
• ai
• cs
• logic
• linguistics
• wp

Quantification, Quantification

For example, in arithmetic, it allows the expression of the statement that every natural number has a successor, and in logic, that something (at least one thing) in the domain of discourse has a certain property, i.e., there exist things with that property in the domain. A language element which generates a quantification is called a quantifier . The resulting expression is a quantified expression, and we say we have quantified over the predicate or function expression whose free variable is bound by the quantifier. Quantification is used in both natural languages and formal languages. Examples of quantifiers in a natural language are: for all , for some , many , few , a lot , and no . In formal languages, quantification is a formula constructor that produces new formulas from old ones.

These concepts are covered in detail in their individual articles; here we discuss features of quantification that apply in both cases.Other kinds of quantification include uniqueness quantification.

He would universally quantify a variable (or relation) by writing the variable over a dimple in an otherwise straight line appearing in his diagrammatic formulas. Frege did not devise an explicit notation for existential quantification, instead employing his equivalent of ~ x ~, or contraposition. Frege's treatment of quantification went largely unremarked until Bertrand Russell's 1903 Principles of Mathematics.

Source: Wikipedia > Quantification