SPECIFYING OPERATIONS FOR NESTED RELATIONS BY RULES AND PARTIAL ORDERS

In this paper rule-based languages over partially ordered nested relations are considered. Starting with ideas of Bancilhons and Koshafians Object Calculus we define a class of purely lattice-based languages, each of them depending on a fixed partial order. We show that for each ordering the semantics of a program can be equivalently defined by minimal model and least fixpoint semantics. Thus our approach is semantically first order. Two well-known orderings - inclusion order and object order - and the corresponding languages are compared in detail. In order to combine the advantages of these two orderings we present a formalism to define more general orderings over so-called Generalized Partitioned Normal Form instances. By examples we demonstrate the expressive power of this approach. Finally, we define the meta-concept modularization that enables us to express operations being non-monotone with respect to each possible partial order. This concept is comparable to the concept of stratification in other approaches, but the basic idea is different.