existential quantifier

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Related to existential quantifiers: universal quantifier

existential quantifier

[‚eg·zə¦sten·chəl ′kwän·tə‚fī·ər]
(mathematics)
A logical relation, often symbolized ∃, that may be expressed by the phrase “there is a” or “there exists”; if P is a predicate, the statement (∃ x) P (x) is true if there exists at least one value of x in the domain of P for which P (x) is true, and is false otherwise.

existential quantifier

References in periodicals archive ?
To eliminate an existential quantifier [exists]z [element of] U, we use the lemma above, by translating its statement into first-order logic.
first-order) existential quantifier. The idea is to maintain that either there is no unrestricted (logical) identity relation at the ground-type or there is no unrestricted first-order existential quantifier.
318) makes a similar proposal for thefirst-order existential quantifier:
In the syntax, only existential quantifiers and disjunctions can be made independent of previous choices (and so only the verifier is handicapped by independence).
The rules for the independent existential quantifier elimination require the introduction of function letters (to express the independence).
Boolos'proposal is to employ plural quantifiers to interpret monadic, second-order existential quantifiers. Construed this way, he claims, a monadic, second-order language has no ontological commitments beyond those of its first-order sub-language.
If both kinds of quantifiers can bind the same sort of variable, then formulas with ordinary existential quantifiers do not obey the standard rules of inference, while formulas with constructibility quantifiers do.