This paper proposes a new way of handling difficult cases of anaphora in language at the level of logical form. This includes donkey anaphora and references into script-like or frame-like knowledge. These cases of anaphora are important, since they occur in virtually every sentence expressing commonsense, general facts about the world - the kinds of facts a language understanding or commonsense reasoning system needs to know. The proposed approach, called "dynamic skolemization', can be implemented within a more-or-less standard logical framework, avoiding the need for logics in which the context of semantic evaluation changes dynamically, such as Discourse Representation Theory or Dynamic Predicate Logic. The approach leads to script-like or frame-like representations, and thus provides a linguistic motivation for them (at the level of complex, structured knowledge rather than at the level of predicate-argument structure).