Existential quantification

Existential quantification
TypeQuantifier
FieldMathematical logic
Statement is true when is true for at least one value of .
Symbolic statement

In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier ("x" or "∃(x)" or "(∃x)"[1]). 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). The existential quantifier is encoded as U+2203 THERE EXISTS in Unicode, and as \exists in LaTeX and related formula editors.

  1. ^ Bergmann, Merrie (2014). The Logic Book. McGraw Hill. ISBN 978-0-07-803841-9.
  2. ^ "Predicates and Quantifiers". www.csm.ornl.gov. Retrieved 2020-09-04.
  3. ^ "1.2 Quantifiers". www.whitman.edu. Retrieved 2020-09-04.
  4. ^ Allen, Colin; Hand, Michael (2001). Logic Primer. MIT Press. ISBN 0262303965.