In problem solving, the decision-theoretic framework is invoked when we wish to define a rich notion of preference over possible solutions. While decision theory provides a clean framwork for representing preference information, eliciting that information can often be difficult. When solutions are simply concrete outcomes, preferences can be represented directly by simply ranking the outcomes. But when solutions can have uncertain outcomes, this is not feasible and preferences are typically represented with a real-valued utility/unction over outcomes, which captures a decision-maker’s atttitudes toward risk. Even in the case of complete certainty, preferences are often represented by a real-valued function over outcomes, called a value/unction.