Parameters for Utilitarian Desires in a Qualitative Decision Theory

In qualitative decision-theoretic planning, desires—qualitative abstractions of utility functions—are combined with defaults—qualitative abstractions of probability distributions—to calculate the expected utilities of actions. This paper is inspired from Lang's framework of qualitative decision theory, in which utility functions are constructed from desires. Unfortunately, there is no consensus about the desirable logical properties of desires, in contrast to the case for defaults. To do justice to the wide variety of desires we define parameterized desires in an extension of Lang's framework. We introduce three parameters, which help us to implement different facets of risk. The strength parameter encodes the importance of the desire, the lifting parameter encodes how to determine the utility of a set (proposition) from the utilities of its elements (worlds), and the polarity parameter encodes the relation between gain of utility for rewards and loss of utility for violations. The parameters influence how desires interact, and they thus increase the control on the construction process of utility functions from desires.