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  2. Existential quantification - Wikipedia

    en.wikipedia.org/wiki/Existential_quantification

    Existential quantification is distinct from universal quantification ("for all"), which asserts that the property or relation holds for all members of the domain. [2] [3] Some sources use the term existentialization to refer to existential quantification. [4] Quantification in general is covered in the article on quantification (logic).

  3. Quantifier (logic) - Wikipedia

    en.wikipedia.org/wiki/Quantifier_(logic)

    As a general rule, swapping two adjacent universal quantifiers with the same scope (or swapping two adjacent existential quantifiers with the same scope) doesn't change the meaning of the formula (see Example here), but swapping an existential quantifier and an adjacent universal quantifier may change its meaning.

  4. Universal quantification - Wikipedia

    en.wikipedia.org/wiki/Universal_quantification

    In symbolic logic, the universal quantifier symbol (a turned "A" in a sans-serif font, Unicode U+2200) is used to indicate universal quantification. It was first used in this way by Gerhard Gentzen in 1935, by analogy with Giuseppe Peano's (turned E) notation for existential quantification and the later use of Peano's notation by Bertrand Russell.

  5. First-order logic - Wikipedia

    en.wikipedia.org/wiki/First-order_logic

    Quantifier symbols: ∀ for universal quantification, and ∃ for existential quantification; Logical connectives: ∧ for conjunction, ∨ for disjunction, → for implication, ↔ for biconditional, ¬ for negation. Some authors [11] use Cpq instead of → and Epq instead of ↔, especially in contexts where → is used for other purposes.

  6. Uniqueness quantification - Wikipedia

    en.wikipedia.org/wiki/Uniqueness_quantification

    In mathematics and logic, the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition. [1] This sort of quantification is known as uniqueness quantification or unique existential quantification, and is often denoted with the symbols "∃!"

  7. Existential theory of the reals - Wikipedia

    en.wikipedia.org/wiki/Existential_theory_of_the...

    the universal quantifier ∀ and the existential quantifier ∃; A sequence of these symbols forms a sentence that belongs to the first-order theory of the reals if it is grammatically well formed, all its variables are properly quantified, and (when interpreted as a mathematical statement about the real numbers) it is a true statement.

  8. Lindström quantifier - Wikipedia

    en.wikipedia.org/wiki/Lindström_quantifier

    Lindström quantifiers generalize first-order quantifiers, such as the existential quantifier, the universal quantifier, and the counting quantifiers. They were introduced by Per Lindström in 1966. They were later studied for their applications in logic in computer science and database query languages .

  9. True quantified Boolean formula - Wikipedia

    en.wikipedia.org/wiki/True_quantified_boolean...

    In computational complexity theory, the language TQBF is a formal language consisting of the true quantified Boolean formulas.A (fully) quantified Boolean formula is a formula in quantified propositional logic (also known as Second-order propositional logic) where every variable is quantified (or bound), using either existential or universal quantifiers, at the beginning of the sentence.