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.)
“But alas! I never could keep a promise. I do not blame myself for this weakness, because the fault must lie in my physical organization. It is likely that such a very liberal amount of space was given to the organ which enables me to make promises, that the organ which should enable me to keep them was crowded out. But I grieve not. I like no half-way things. I had rather have one faculty nobly developed than two faculties of mere ordinary capacity.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“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)
“There isn’t any universal reason;
And no one but a man would think there was.
You don’t catch women trying to be Plato.”
—Robert Frost (1874–1963)