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Quantifiers

  • Two quantifiers: Universal (∀) and Existential (∃)

  • Allow us to express properties of collections of objects instead of enumerating objects by name

    • Apply to sentence containing variable

  • Universal ∀: true for all substitutions for the variable

    • “for all”: ∀

  • Existential ∃: true for at least one substitution for the variable

    • “there exists”: ∃

  • Examples:

    • ∃ x: Mother(art) = x

    • ∀ x ∀ y: Mother(x) = Mother(y) → Sibling(x,y)

    • ∃ y ∃ x: Mother(y) = x


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