 We say that a formula \(\varphi\) of \(\scrL_\Box\) is true in an SQML interpretation \(\calM\) for \(\scrL_\Box\) if it is true\(_{w^\ast}^\calM\), i.e., true in \(\calM\) at the “actual world” \(w^\ast\) of \(\calM\). Satisfiability and logical truth are defined exactly as they are  above  for classical predicate logic, albeit relative to modal languages \(\scrL_\Box\) and the preceding notion of truth in an SQML interpretation; in particular, a formula \(\varphi\) of \(\scrL_\Box\) is logically true if it is true in every SQML interpretation. The logic so defined is, of course, SQML.