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.

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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]\displaystyle{ \Omega }[/math] be a set of worlds, each world [math]\displaystyle{ w \in \Omega }[/math] being a truth-value assignment to a finite set of atomic variables [math]\displaystyle{ (X_1, X_2, … ,X_n) }[/math] which in this paper we assume to be hi-valued, namely, [math]\displaystyle{ X_i \in {true, false} }[/math]. A belief ranking function [math]\displaystyle{ \kappa(w) }[/math] is an assignment of non-negative integers to the elements of [math]\displaystyle{ \Omega }[/math] such that [math]\displaystyle{ \kappa(w) = 0 }[/math] for at least one [math]\displaystyle{ w \in \Omega }[/math]. Intuitively, [math]\displaystyle{ \kappa(w) }[/math] represents the degree of surprise associated with finding a world [math]\displaystyle{ w }[/math] realized, and worlds assigned [math]\displaystyle{ \kappa = 0 }[/math] are considered serious possibilities. [math]\displaystyle{ \kappa(w) }[/math] can be considered an order-of-magnitude approximation of a probability function [math]\displaystyle{ P(w) }[/math] by writing [math]\displaystyle{ P(w) }[/math] as a polynomial of some small quantity f and taking the most significant term of that polynomial,

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