On specialization constraints over complex objects

Abstract

Most semantic data models and object-oriented data models allow entity and object classes to be organized according to a generalization taxonomy. In addition, range restrictions (or property typing) may be specified not only on properties associated with a given class, but also on properties inherited from superclasses. In this paper, we consider a more general form of specialization constraint in which range restrictions are associated with property value paths, instead of with the properties themselves. One consequence is that the constraints enable a form of molecular abstraction, in which the internals of more complicated objects can be defined in terms of a collection of more primitive classes.

We consider the problem for two models. The first imposes no constraints on class membership for an object beyond those implied by sub-classing constraints. In this case, we present a sound and complete axiomatization for arbitrary specialization constraints, and efficient decision procedures for the corresponding membership problems. The second model is more typical and requires that each object is created with respect to a particular class. Membership problems in this case are shown to be NP-hard, and NP-complete if class schema include a "bottom" class. We exhibit polynomial-time decision procedures when a bottom class does exist and antecedent specialization constraints satisfy a bounded path length condition.

We also consider a case concerning the second model in which class schema satisfy a lower semi-lattice condition. A sound and complete axiomatization for well-formed specialization constraints is presented, together with efficient decision procedures for the membership problem for well-formed constraints, and for determining if an arbitrary constraint is well-formed. We prove that the membership problem for arbitrary specialization constraints remains NP-complete, however, even for class schema satisfying the lower semi-lattice condition.