Revisiting Conditional Preferences: From Defaults to Graphical Representations

A conditional preference statement takes the form "in context c, a is preferred to not a". It is quite similar to the piece of knowledge "if c is true, a is more plausible than not a", which is a standard way of understanding the default rule "if c then generally a". A set of such defaults translates into a set of constraints that can be represented in the setting of possibility theory. The application of a minimum specificity principle, natural when handling knowledge, enables us to compute a priority ranking between possible worlds. The paper investigates if a similar approach could be applied to preferences as well. Still in this case, the use of a maximum specificity principle is as natural as the converse principle, depending on the decision maker attitude in terms of pessimism or optimism. The paper studies the differences between this approach and qualitative graphical approaches to preference modeling such as p-pref-nets (based on possibility theory) and CP-nets (relying on ceteris paribus principle). While preferences in a conditional preference network can always be expressed as "default-like" constraints, there are cases where "non monotonic" preferences cannot be associated with a preference network structure, but can still be dealt with as constraints. When both approaches can be applied, they may lead to different orderings of solutions. The paper discusses this discrepancy and how to remedy it.