Expressible preferential logics.

We introduce expressible preferential logics, whose preference relations can be defined by some abstract logic. Abstract logics not only allow one to describe preference relations, but also classes of abstract preferential logics and give general proofs for properties common to all logics in these classes. Our approach follows that of Abstract Model Theory. We show that some well-known non-monotonic logics are preferential. We prove that they are elementary, which means that their preference relation can be defined in first-order logic. We study expressiveness and definability results for wide classes of abstract preferential logics in the spirit of Universal Logic. We present a collapse result for expressible preferential logics. We prove that, for a class of expressible preferential logics, if the class of minimal models of a finite set of sentences is Δ-L-expressible, then it is L-expressible, i.e. such class of models can be finitely axiomatized in L. Using this result, we show that under certain conditions one can axiomatize the class ℂ of minimal models of a finite set of sentences where some symbol P is defined using that set and an explicit definition for this symbol. [ABSTRACT FROM AUTHOR]