Logical Quantification
A Logical Quantification is a Predicate Logic that specifies the quantity of specimens in Discourse Domain that satisfy an open formula.
- AKA: Logic Quantifier.
- Context
- it ranges from being an Universal Quantification Operator ([math]\displaystyle{ \forall }[/math]) to being an Existential Quantification Operator ([math]\displaystyle{ \exists }[/math]).
- Example(s):
- Counter-Example(s):
- See: Logic, Domain of Discourse, Free Variable, Bound Variable, Semantics, Turned A, Turned E, Andrzej Mostowski, Quantifier Elimination.
References
2019
- (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Quantifier_(logic) Retrieved:2019-8-24.
- In logic, quantification specifies the quantity of specimens in the domain of discourse that satisfy an open formula. The two most common quantifiers mean “for all” and “there exists”. For example, in arithmetic, quantifiers allow one to say that the natural numbers go on forever, by writing that for all n (where n is a natural number), there is another number (say, the successor of n) which is one bigger than n.
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 specify 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.
Quantification is used as well in natural languages; examples of quantifiers in English are for all, for some, many, few, a lot, and no; see Quantifier (linguistics) for details.
- In logic, quantification specifies the quantity of specimens in the domain of discourse that satisfy an open formula. The two most common quantifiers mean “for all” and “there exists”. For example, in arithmetic, quantifiers allow one to say that the natural numbers go on forever, by writing that for all n (where n is a natural number), there is another number (say, the successor of n) which is one bigger than n.