Axiomatic Specification of Database Domain Statics

In the past ten years, much work has been done to add more structure to database models 1 than what is represented by a mere collection of flat relations (Albano & Cardelli [1985], Albano et al. [1986], Borgida eta. [1984], Brodie [1984], Brodie & Ridjanovic [1984], Brodie & Silva (1982], Codd (1979], Hammer & McLeod (1981], King (1984], King & McLeod [1984], [1985], Mylopoulos et al. [1980], Smith & Smith 1977a & b). 2 The informal approach which most of these studies advocate has a number of disadvantages. First, a recent survey of some of the pro­ posed models by Urban & Delcambre [1986] reveals a wide divergence in terminology and con­ cepts, making comparison of the expressive power of these models difficult. Second, undefined or even ill-defined concepts are a hindrance, not an aid, for the analysis of the Universe of Discourse (UoD). Third, informal treatment 9f such complex structures as set hierarchies, gen­ eralization hierarchies and aggregation hierarchies all in one model, with some dynamics thrown in for good measure, bodes ill for the consistency of these theories. The first goal of the research reported on is to integrate the static structures which these models propose in one coherent, axiomatic framework. It will be shown in chapter 7 that the theory presented here provides the needed conceptual foundations for these models. A second aim is to provide a possible worlds framework onto which to graft theories of the dynamics of the UoD. The third aim is to provide clear concepts which can aid the database model designer in his or her thinking about the UoD. In this report we concentrate on the first goal only, leav­ ing the formulation of theories of domain dynamics and the application to system development as research goals for the near future