  CP-nets represent the dominant existing framework for expressing qualitative
conditional preferences between alternatives, and are used in a variety of
areas including constraint solving. Over the last fifteen years, a significant
literature has developed exploring semantics, algorithms, implementation and
use of CP-nets. This paper introduces a comprehensive new framework for
conditional preferences: logical conditional preference theories (LCP
theories). To express preferences, the user specifies arbitrary (constraint)
Datalog programs over a binary ordering relation on outcomes. We show how LCP
theories unify and generalize existing conditional preference proposals, and
leverage the rich semantic, algorithmic and implementation frameworks of
Datalog.
