  Logical formalisms provide a natural and concise means for specifying and
reasoning about preferences. In this paper, we propose lexicographic logic, an
extension of classical propositional logic that can express a variety of
preferences, most notably lexicographic ones. The proposed logic supports a
simple new connective whose semantics can be defined in terms of finite lists
of truth values. We demonstrate that, despite the well-known theoretical
limitations that pose barriers to the quantitative representation of
lexicographic preferences, there exists a subset of the rational numbers over
which the proposed new connective can be naturally defined. Lexicographic logic
can be used to define in a simple way some well-known preferential operators,
like "$A$ and if possible $B$", and "$A$ or failing that $B$". Moreover, many
other hierarchical preferential operators can be defined using a systematic
approach. We argue that the new logic is an effective formalism for ranking
query results according to the satisfaction level of user preferences.
