 Nonrigid designators, if empty at some worlds, require free logics even with fixed domains. (Thus classical logic with nonrigid designators is possible only if we require for each singular term \(t\) that at each world \(w\), \(t\) denotes some object in \(\bD_w\).) On some semantics for nonrigid designators, the quantifier rule must differ from that given above, and other adjustments must be made. For details, see Garson 1991, Cocchiarella 1991, Schweitzer 2001 and Simons 2001.