Glossary:Universal Quantifier

Universal Quantifier

BE /ˌju:nɪˈvɜ:səl ˈkwɒntɪfaɪə/, AE /ˌjunəˈvɜrsəl ˈkwɑntɪˌfaɪər/

Definition

The universal quantifier (symbolized by the operator ∀) is used to mean that the statement is true for every entity in the domain in question and is conveyed by such expressions as all, every and each.

Examples

Every dog is barking.
∀x (DOG (x) → BARK (x))
“For every thing x, if x is a dog then x is barking.”

All students were tired.
∀x (STUDENT (x) → TIRED (x))
“For every thing x, if x is a student then x is tired.”

References

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

Related Terms

• Existential Quantifier
• Logical Form
• Logical Operator (Propositional Connective)
• Logical Quantifier
• Predicate Logic (First-order Logic)
• Quantifier
• Restricted Quantifier
• Variable

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