  Richard Cox [1] set the axiomatic foundations of probable inference and the
algebra of propositions. He showed that consistency within these axioms
requires certain rules for updating belief. In this paper we use the analogy
between probability and utility introduced in [2] to propose an axiomatic
foundation for utility inference and the algebra of preferences. We show that
consistency within these axioms requires certain rules for updating preference.
We discuss a class of utility functions that stems from the axioms of utility
inference and show that this class is the basic building block for any general
multiattribute utility function. We use this class of utility functions
together with the algebra of preferences to construct utility functions
represented by logical operations on the attributes.
