 If one is not interested in knowledge and belief collapsing, one must thus give something up: One cannot have both 5 for knowledge, D for belief and KB1 and KB3 governing their interaction. Again, results concerning correspondence between principles and relation properties may assist: In 1993, van der Hoek showed based on a semantic analysis that where the four principles are jointly sufficient for collapse, no subset of them is, too. Giving up any one principle will thus eliminate the collapse. Weakening KB1 to hold only for non-modal formulas is also sufficient to avoid collapse (cf. Halpern 1996).