 The definition of truth simpliciter above for formulas of an applied non-modal language \(\scrL\) stems from the fact that a Tarskian interpretation \(\calI\) for \(\scrL\) can take the things in (some relevant chunk of) the actual world and represent how they actually exemplify the properties and relations expressed by the predicates of \(\scrL\). But if we can represent the actual world (or a relevant chunk of it) by means of an intended Tarskian interpretation, then there is no reason that we can’t represent a merely possible world in which those same things exist but have different properties and stand in different relations and, hence, define objective notions of truth at a world and of truth simpliciter for the formulas of a modal language as well, that is, notions of truth that are not simply relative to formal, mathematical interpretations but, rather, correspond to objective modal reality. So let \(\scrL_\Box\) be an applied modal language whose individual constants and predicates represent those in some ordinary range of modal discourse and let \(D\) be its intended domain. Say that \(\calM\) is an intended interpretation of \(\scrL_\Box\) if