 We should also note that one alternative semantic picture for SDL is where we have a set of world-relative ordering relations, one for each world \(i\) in W, where \(j \ge_i k\) iff \(j\) is as good as \(k\) (and perhaps better) relative to \(i\). We might then assume that from the standpoint of any world \(i\), a) each world is as good as itself, b) if one is as good as a second, and the second is as good as a third, then the first is as good as the third, c) and for any two worlds, either the first is as good as the second or vice versa (i.e., respectively, each such \(\ge_i\) is reflexive, transitive, and connected in W). As a matter of fact, this approach also determines SDL. (See Goble 2003 for one of the few proofs of this claim.) If we then add “The Limit Assumption”, that for each world \(i\), there is always at least one world as good as all worlds (i.e., one \(i\)-best world) we can easily generate our earlier semantics for SDL derivatively. We need only add the natural analogue here to our prior truth-conditions for \(\OB\): \(\OB p\) is true at a world \(i\) iff \(p\) is true at all the \(i\)-best worlds: