1993 FromConditionalOughtstoQualitat

(Pearl, 1993) ⇒ Judea Pearl. (1993). “From Conditional Oughts to Qualitative Decision Theory.” In: Proceedings of the Ninth International Conference on Uncertainty in artificial intelligence.

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Abstract

The primary theme of this investigation is a decision theoretic account of conditional ought statements (e.g., "You ought to do A, if C”) that rectifies glaring deficiencies in classical deontic logic. The resulting account forms a sound basis for qualitative decision theory, thus providing a framework for qualitative planning under uncertainty. In particular, we show that adding causal relationships (in the form of a single graph) as part of an epistemic state is sufficient to facilitate the analysis of action sequences, their consequences their interaction with observations, their expected utilities and, hence, the synthesis of plans and strategies under uncertainty.

2. INFINITESIMAL PROBABILITIES, RANKING FUNCTIONS, CAUSAL NETWORKS, AND ACTIONS

1. (Ranking Functions).

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, i.e., …

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	Author	volume	Date Value	title	type	journal	titleUrl	doi	note	year
1993 FromConditionalOughtstoQualitat	Judea Pearl			From Conditional Oughts to Qualitative Decision Theory