Database Logic was proposed in the late 1970's as a generalization of first-order logic in order to deal in a uniform manner with relational, hierarchic, and network databases. At about the same time, the study of deductive (relational) databases has become important, primarily as a vehicle for the development of expert database systems. Also, Prolog, the main logic programming language, has become prominent for many applications in artificial intelligence, and its connections with deductive databases have been investigated. Although the relational model provides a suitable framework for traditional, essentially data processing applications, several researchers have found the need for complex objects in newer applications, such as engineering databases. In this paper we show how database logic can be extended in two directions: 1) to include complex objects, and 2) to provide deductive capabilities for hierarchic and network databases.