Propositional distances and compact preference representation

Distances between possible worlds play an important role in logic-based knowledge representation (especially in belief change, reasoning about action, belief merging and similarity-based reasoning). We show here how they can be used for representing in a compact and intuitive way the preference profile of an agent, following the principle that given a goal G, then the closer a world w to a model of G, the better w. We give an integrated logical framework for preference representation which handles weighted goals and distances to goals in a uniform way. Then we argue that the widely used Hamming distance (which merely counts the number of propositional symbols assigned a different value by two worlds) is generally too rudimentary and too syntax-sensitive to be suitable in real applications; therefore, we propose a new family of distances, based on Choquet integrals, in which the Hamming distance has a position very similar to that of the arithmetic mean in the class of Choquet integrals.