 Here we begin to see the logical challenge that confronts the actualist: a logically valid principle of SQML—in this case, a standard principle of classical logic—is rendered invalid when we attempt to revise our modal semantics so as to accommodate actualist intuitions. The challenge is then how (or whether) to revise the principle in question, and this in turn often requires a choice between several competing possibilities, each of which may require further revisions still. Kripke himself avoids several options that might suggest themselves in light of the invalidity of Q2 in KQML. For instance, taking a lead from Prior (1957: 33–35), an actualist might argue that terms—individual constants and variables (when they occur freely)—are directly referring expressions like proper names and demonstratives and, hence, that an accurate model theoretic representation of actualism should require that the value \(\tau^\calK\) that \(\calK\) assigns to an arbitrary term \(\tau\) should be restricted to the domain of the actual world \(w^\ast\) of \(\calK\)—one cannot, after all, refer to individuals that don’t actually exist. This modification of KQML would indeed preserve the validity of Q2 but at the cost of invalidating Nec—notably, it would render the inference from line 1 to line 2 in the above proof invalid. For, while line 1 might now be true at the actual world \(w^\ast\) of an arbitrary interpretation \(\calK\) because we’ve stipulated that \(\sfx^\calK\) exist in \(w^\ast,\) that very fact could well render line 1 false at some other world \(u\): \(\forall \sfx \Box \neg \sfB\sfx\) might be true at \(u\) but our actually existing individual \(\sfx^\calK,\) although not in the extension of \(\sfB\) in the actual world, might well be in its extension at \(u\). So, under the proposed modification, the question for the actualist instead becomes how to modify Nec—perhaps by limiting how it applies to formulas involving individual constants and free variable occurrences in some  way.[57]