About: Quantifier (logic)

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In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier in the first order formula expresses that everything in the domain satisfies the property denoted by . On the other hand, the existential quantifier in the formula expresses that there is something in the domain which satisfies that property. A formula where a quantifier takes widest scope is called a quantified formula. A quantified formula must contain a bound variable and a subformula specifying a property of the referent of that variable.

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rdf:type	Thing
rdfs:label	Quantifier (logic) (en)
rdfs:comment	In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier in the first order formula expresses that everything in the domain satisfies the property denoted by . On the other hand, the existential quantifier in the formula expresses that there is something in the domain which satisfies that property. A formula where a quantifier takes widest scope is called a quantified formula. A quantified formula must contain a bound variable and a subformula specifying a property of the referent of that variable. (en)
rdfs:seeAlso	Fubini's theorem
sameAs	Quantifier (logic)
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Subject	Philosophical logic Predicate logic Quantifier (logic) Semantics Logic
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Quantifier_(logic)?oldid=1074047095&ns=0
Wikipage page ID	43507260 (xsd:integer)
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has abstract	In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier in the first order formula expresses that everything in the domain satisfies the property denoted by . On the other hand, the existential quantifier in the formula expresses that there is something in the domain which satisfies that property. A formula where a quantifier takes widest scope is called a quantified formula. A quantified formula must contain a bound variable and a subformula specifying a property of the referent of that variable. Every formula in classical logic can be rewritten as a logically equivalent quantified formula in prenex normal form, where every quantifier takes the widest scope. The mostly commonly used quantifiers are and . These quantifiers are standardly defined as duals and are thus interdefinable using negation. They can also be used to define more complex quantifiers, as in the formula which expresses that nothing has the property . Other quantifiers are only definable within second order logic or higher order logics. Quantifiers have been generalized beginning with the work of Mostowski and Lindström. First order quantifiers approximate the meanings of some natural language quantifiers such as "some" and "all". However, many natural language quantifiers can only be analyzed in terms of generalized quantifiers. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Quantifier_(logic)
is notableIdea of	Bertrand Russell
is Wikipage redirect of	Logical quantifier Quantification (logic) Quantificational fallacy Quantifiers (logic) Set quantifier Range of quantification Solution quantifier
is Link from a Wikipage to another Wikipage of	Formation rule Foundations of mathematics Logic Logic Logical constant Logical hexagon Logical quantifier Logical truth Nominalism Non-logical symbol Nondeterministic constraint logic Nonstandard calculus Absolute generality Abstract object theory Accident (fallacy) Actualism Adjoint functors Albert of Saxony (philosopher) Alexander Zinoviev Alfred Tarski Algebraic theory Alloy (specification language) Artificial intelligence Atomic formula Atomic sentence Axiom of determinacy Bertrand Russell Logic gate Boolean satisfiability problem Bounded arithmetic Branching quantifier Categorical quantum mechanics Frederick Parker-Rhodes Free variables and bound variables General set theory Generalized quantifier Gentzen's consistency proof George Bentham George Boole Glossary of artificial intelligence Joseph Sgro Dieter Rödding Domain of discourse Duality (mathematics) History of logic History of mathematical notation Metatheorem Method of analytic tableaux Church's thesis (constructive mathematics) Classical logic Cylindric algebra De Interpretatione De dicto and de re Definite description Deflationary theory of truth Hyperreal number List of fallacies Combinatory logic Constructible universe Constructive set theory

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