5 beyond K(m)/alc

Although we do not yet have any empirical evidence backing our claim, we believe that our method will work for a wide class of logics, and, more speciically with most (all?) normal modal logics. First, independently on the logic considered, L monotonically increases the constraintness of the formulae, decreasing their satissa-bility probability, causing thus a satissability transition. Diierent logics can only aaect the location and the steep-ness of the transition itself: the higher the logic in the hierarchy of normal modal logics, the more likely unsat-issable the formula, the earlier the transition. Second, the last consideration in Section 4.2 (see also Williams and Hogg, 1994]) suggests that easy-hard-easy patterns in the size of the search space are also a direct consequence of the monotonic increase of constraintness, independently on the kind of logic considered. Again, diier-ent logics can only aaect the location and the steepness of the peak itself. We have performed an analogous (unpublished) set of experiments for modal S5, in which we have obtained results qualitatively similar | but a little shifted to the left, as expected | to those of Giunchiglia and Sebastiani, 1996a]. We expect easy-hard-easy patters centered in the satissability transition zone will exist for most (all?) modal normal logics. There is a natural way to extend our method to logics which extend the syntax of K(m)/ALC with other