# Belief Ranking Function

A Belief Ranking Function is a ranking function whose input domain are beliefs and whose output range is a truth-value assignment.

**See:**True Belief, False Belief, Belief Revision.

## References

### 1993

- (Pearl, 1993) ⇒ Judea Pearl. (1993). “From Conditional Oughts to Qualitative Decision Theory.” In: Proceedings of the Ninth International Conference on Uncertainty in artificial intelligence.
- QUOTE: Let [math]\Omega[/math] be a set of worlds, each world [math]w \in \Omega[/math] being a truth-value assignment to a finite set of atomic variables [math](X_1, X_2, … ,X_n)[/math] which in this paper we assume to be hi-valued, namely, [math]X_i \in {true, false}[/math]. A belief
*ranking function*[math]\kappa(w)[/math] is an assignment of non-negative integers to the elements of [math]\Omega[/math] such that [math]\kappa(w) = 0[/math] for at least one [math]w \in \Omega[/math]. Intuitively, [math]\kappa(w)[/math] represents the degree of surprise associated with finding a world [math]w[/math] realized, and worlds assigned [math]\kappa = 0[/math] are considered serious possibilities. [math]\kappa(w)[/math] can be considered an order-of-magnitude approximation of a probability function [math]P(w)[/math] by writing [math]P(w)[/math] as a polynomial of some small quantity f and taking the most significant term of that polynomial,

- QUOTE: Let [math]\Omega[/math] be a set of worlds, each world [math]w \in \Omega[/math] being a truth-value assignment to a finite set of atomic variables [math](X_1, X_2, … ,X_n)[/math] which in this paper we assume to be hi-valued, namely, [math]X_i \in {true, false}[/math]. A belief