Whereas probability theory uses a single number, the probability, to describe how likely an event is to occur, possibility theory uses two concepts, the possibility and the necessity of the event. For any set, the necessity measure is defined by
In the above formula, denotes the complement of, that is the elements of that do not belong to . It is straightforward to show that:
- for any
and that:
Note that contrary to probability theory, possibility is not self-dual. That is, for any event, we only have the inequality:
However, the following duality rule holds:
- For any event, either, or
Accordingly, beliefs about an event can be represented by a number and a bit.
Read more about this topic: Possibility Theory
Famous quotes containing the word necessity:
“I have no purpose to introduce political and social equality between the white and black races. There is a physical difference between the two, which, in my judgement, will probably for ever forbid their living together upon the footing of perfect equality; and inasmuch as it becomes a necessity that there must be a difference, I ... am in favour of the race to which I belong having the superior position.”
—Abraham Lincoln (1809–1865)
“Nothing in the universe is contingent, but all things are conditioned to exist and operate in a particular manner by the necessity of the divine nature.”
—Baruch (Benedict)
“The sadness of the women’s movement is that they don’t allow the necessity of love. See, I don’t personally trust any revolution where love is not allowed.”
—Maya Angelou (b. 1928)