Universal Quantification Operation

A Universal Quantification Operation is a predicate logic quantification operation that requires a Predicate Sentence to be True for every possible Variable Member of a Logic Variable.

• AKA: ∀, ForAll.
• Example(s):
  • [math]\displaystyle{ X \land Y \Rightarrow \forall x \in X, X \land Y }[/math].
  • ...
  • …
• Counter-Example(s):
  • an Existential Quantification Operation, such as [math]\displaystyle{ X \land Y \Rightarrow \exists x \in X, X \land Y }[/math].
• See: Generalised Function Space.

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References

2013

• (Wikipedia, 2013) ⇒ http://en.wikipedia.org/wiki/Universal_quantification
  • In predicate logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all". It expresses that a propositional function can be satisfied by every member of a domain of discourse. In other terms, it is the predication of a property or relation to every member of the domain. It asserts that a predicate within the scope of a universal quantifier is true of every value of a predicate variable.

    It is usually denoted by the turned A (∀) logical operator symbol, which, when used together with a predicate variable, is called a universal quantifier ("∀x", "∀(x)", or sometimes by "(x)" alone). Universal quantification is distinct from existential quantification ("there exists"), which asserts that the property or relation holds only for at least one member of the domain.

    Quantification in general is covered in the article on quantification. Symbols are encoded Template:Unichar.

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