Glossary:Existential Quantifier: Difference between revisions

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==Definition==
==Definition==
The existential quantifier (symbolized by the operator ∃) is used to mean that the statement is true of at least one entity in the domain and stands for expressions with a/an (one), some and there is.
The existential quantifier (symbolized by the '''operator ∃''') is used to mean that the statement is true of '''at least one entity''' in the domain and stands for expressions with '''''a/an (one), some''''' and '''''there is'''''.


==Examples==
==Examples==


A dog barked. <br/>
A dog barked. <br/>
∃x (DOG (x) & BARK (x)) <br/>
'''∃x (DOG (x) & BARK (x))''' <br/>
“There is at least one thing x such that x is a dog and x barked.” <br/>
''“There is at least one thing x such that x is a dog and x barked.”'' <br/>


Some birds were singing. <br/>
Some birds were singing. <br/>
∃x (BIRD (x) & SING (x)) <br/>
'''∃x (BIRD (x) & SING (x))''' <br/>
“There is at least one thing x such that x is a bird and x sings.” <br/>
''“There is at least one thing x such that x is a bird and x sings.”'' <br/>


==References==
==References==
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==Related Terms==
==Related Terms==
Logical Form
* [[Glossary:Logical Form | Logical Form]]
Logical Quantifier
* [[Glossary:Logical Operator | Logical Operator (Propositional Connective)]]
Logical Symbol
* [[Glossary:Logical Quantifier | Logical Quantifier]]
Predicate Logic (First-order Predicate Logic)
* [[Glossary:Predicate logic| Predicate Logic (First-order Logic)]]
Quantifier
* [[Glossary:Quantifiers | Quantifier]]
Restricted Quantifier
* [[Glossary:Restricted Quantifier | Restricted Quantifier]]
Universal Quantifier
* [[Glossary:Universal Quantifier| Universal Quantifier]]
Variable
* [[Glossary:Variable | Variable]]
 
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Latest revision as of 01:51, 24 June 2016

Existential Quantifier

BE /ˌɛgzɪˈstɛnʃəl ˈkwɒntɪfaɪə/, AE /ˌɛgˌzɪˈstɛnʧəl ˈkwɑntɪˌfaɪər/

Definition

The existential quantifier (symbolized by the operator ∃) is used to mean that the statement is true of at least one entity in the domain and stands for expressions with a/an (one), some and there is.

Examples

A dog barked.
∃x (DOG (x) & BARK (x))
“There is at least one thing x such that x is a dog and x barked.”

Some birds were singing.
∃x (BIRD (x) & SING (x))
“There is at least one thing x such that x is a bird and x sings.”

References

  • Gregory, Howard. 2000. Semantics. Language Workbook. London/New York: Rutledge.
  • Riemer, Nick. 2010. Introducing Semantics. Cambridge [et al.]: Cambridge University Press.

Related Terms


Back to the Basic Glossary