The Algebra of Utility Inference

Abstract

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.