Variable sets and functions framework for conceptual modeling: Integrating ER and OO via sketches with dynamic markers

In the paper a graph-based specification language for semantic modeling is proposed. It is as handy as conventional graphical languages but, in contrast to them, possesses a precisely formalized semantics based on certain ideas of the mathematical category theory. In particular, it provides mathematically correct semantics for formerly somewhat mythical notions of object identity and weak entity type. Among other benefits of the approach there are provable (!) universality w.r.to simulation of any other formal data specification, flexibility and unification in treating various kinds of associations and relationships, precise semantic basis for the familiar distinguishing between the specialization and generalization ISA-relationships, intrinsic object-orientedness.