Reduction To Ordinary Existential and Universal Quantification
Uniqueness quantification can be expressed in terms of the existential and universal quantifiers of predicate logic by defining the formula ∃!x P(x) to mean
where an equivalence is:
An equivalent definition that has the virtue of separating the notions of existence and uniqueness into two clauses, at the expense of brevity, is
Another equivalent definition with the advantage of brevity is
Read more about this topic: Uniqueness Quantification
Famous quotes containing the words reduction, ordinary, existential and/or universal:
“The reduction of nuclear arsenals and the removal of the threat of worldwide nuclear destruction is a measure, in my judgment, of the power and strength of a great nation.”
—Jimmy Carter (James Earl Carter, Jr.)
“The Taylor and the Painter often contribute to the Success of a Tragedy more than the Poet. Scenes affect ordinary Minds as much as Speeches; and our Actors are very sensible, that a well-dressed Play has sometimes brought them as full Audiences, as a well-written one.... But however the Show and Outside of the Tragedy may work upon the Vulgar, the more understanding Part of the Audience immediately see through it, and despise it.”
—Joseph Addison (1672–1719)
“One of the most horrible, yet most important, discoveries of our age has been that, if you really wish to destroy a person and turn him into an automaton, the surest method is not physical torture, in the strict sense, but simply to keep him awake, i.e., in an existential relation to life without intermission.”
—W.H. (Wystan Hugh)
“Let us build altars to the Blessed Unity which holds nature and souls in perfect solution, and compels every atom to serve an universal end.”
—Ralph Waldo Emerson (1803–1882)