Traditional database query algebras usually have only one special sort to describe database and result structures, for example the sort `relation' in relational algebra. For the new developments concerning object-oriented and extensible database systems, it seems to be more appropriate to define a many-sorted algebra based on several primitive domain algebras and type constructors like sets or lists. In this paper, we present the denotational semantics of QUAL expressions using an abstract data type framework. QUAL is a many-sorted query algebra defined as a query formalism for the structural part of the OBLOG object model. The abstract data type semantics of QUAL allows easy extension of the structural part of OBLOG models by new domain data types and new type constructors.