Although lists, trees, and directed acyclic graphs (dags) are of fundamental interest in computer science, they have scarcely been noticed as data types by existing database systems and database models. In this article I present query language concepts for (object-oriented) database systems offering such non-traditional data resp. object types. For the main task of such a query language, namely the specification of predicates on instances of these types, a temporal logic approach is used. For this, an existing timely oriented approach for querying lists is extended by incorporating concepts from the area of branching-time logics. This article mainly presents the logic concepts of the query language and an implementation of these concepts in an object base systems for discrete structures.