Tagging as an alternative to object creation

Abstract

Based on the observation that graphs play an important role in the representation of databases, an algebra is presented for the manipulation of binary relations, i.e., of directed unlabeled graphs. This so-called Tarski algebra is based on early work by Tarski. The key notion that has been added to it here is tagging, which is needed for providing both enough querying power. Moreover, tagging can also be seen as a value-based counterpart to object creation in object-oriented data models. We present tagging in a general formal framework that incorporates several specific tagging strategies as a special case. We show that each of these strategies allows for the simulation in the Tarski model of various other database models, in particular of the relational model. Finally, we discuss the genericity of tagging and show that the Tarski algebra augmented with multiple assignments and a while-construct is a computationally complete database language.