Generalised Sketches as an algebraic graph-based framework for semantic modeling and database design

A graph-based speciication language and the corresponding machinery are described as stating a basic framework for semantic modeling and database design. It is shown that a few challenging theoretical questions in the area, and some of hot practical problems as well, can be successfully approached in the framework. The machinery has its origin in the classical sketches invented by Ehresmann and is close to their generalization recently proposed by Makkai. There are two essential distinctions from Makkai's sketches. One consists in a diierent { more direct { formalization of sketches that categorists (and database designers) usually draw. The second distinction is more fundamental and consists in introducing operational sketches specifying complex diagram operations over ordinary (predicate) sketches, correspondingly, models of operational sketches are diagram algebras. Together with the notion of parsing operational sketches, this is the main mathematical contribution of the paper. It is demonstrated that it gives rise to a proper design of graphical query languages. On the other hand, the machinery presents an immediate formaliza-tion of diagram chasing { the major tool of categorical reasoning and, hopefully, of the nearest future semantic modeling techniques.