Glossary:Existential Quantifier: Difference between revisions
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(Created page with "=Existential Quantifier= BE /ˌɛgzɪˈstɛnʃəl ˈkwɒntɪfaɪə/, AE /ˌɛgˌzɪˈstɛnʧəl ˈkwɑntɪˌfaɪər/ ==Definition== The existential quantifier (symbolized by...") |
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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 | * [[Glossary:Logical Quantifier | Logical Quantifier]] | ||
Predicate Logic (First-order | * [[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
- Logical Form
- Logical Operator (Propositional Connective)
- Logical Quantifier
- Predicate Logic (First-order Logic)
- Quantifier
- Restricted Quantifier
- Universal Quantifier
- Variable
Back to the Basic Glossary