A Database Interface for Complex Objects

We describe a formal design for a logical query language using psi-terms as data structures to interact effectively and efficiently with a relational database. The structure of psi-terms provides an adequate representation for so-called complex objects. They generalize conventional terms used in logic programming: they are sorted attributed structures, ordered thanks to a subsort ordering. Unification of psi-terms is an effective means for integrating multiple inheritance and partial information into a deduction process. We define a compact database representation for psi-terms, representing part of the subsorting relation in the database as well. We describe a retrieval algorithm based on an abstract interpretation of the psi-term unification process and prove its formal correctness. This algorithm is efficient in that it incrementally retrieves only additional facts that are actually needed by a query, and never retrieves the same fact twice.