An important characteristic of many logics for Artificial Intelligence is
their nonmonotonicity. This means that adding a formula to the premises can
invalidate some of the consequences. There may, however, exist formulae that
can always be safely added to the premises without destroying any of the
consequences: we say they respect monotonicity. Also, there may be formulae
that, when they are a consequence, can not be invalidated when adding any
formula to the premises: we call them conservative. We study these two classes
of formulae for preferential logics, and show that they are closely linked to
the formulae whose truth-value is preserved along the (preferential) ordering.
We will consider some preferential logics for illustration, and prove syntactic
characterization results for them. The results in this paper may improve the
efficiency of theorem provers for preferential logics.Comment: See http://www.jair.org/ for any accompanying file
