 All three of the controversial logical truths of SQML—BF, CBF, and \(\Box\textbf{N}\)—are invalid in KQML, that is, in KQML, they are not logically true. The key in each case is KQML’s modification of the way that quantified formulas are evaluated at worlds. As we saw in  §3.3  above, the validity of BF in SQML—its truth in every interpretation—depends essentially on the fact that, in evaluating an existentially quantified formula \(\exists\nu\varphi\) at an arbitrary possible world \(w,\) the initial occurrence of \(\exists\nu\) in the formula ranges unrestrictedly over all individuals. In KQML, by contrast, the range of the initial quantifier \(\exists\nu\) is restricted to \(\textit{dom}(w),\) to the individuals that exist in \(w\). And, because what exists can vary from world to world, this renders BF invalid: from the fact that some world and some individual existing in that world are thus and so it certainly does not follow that some individual existing in the actual world and some world are thus and so. Notably, while in some worlds there are children of Bergoglio, nothing here in the actual world is a child of Bergoglio in any world, i.e., \(\Diamond\exists \sfx\, \sfB\sfx\) is true and \(\exists \sfx\Diamond \sfB\sfx\) is false. Hence, the BF instance