Object-Role Modeling and Finite-Model Theory

Why a proof theoretic mapping of greater Object-Role Modeling to a theory under finite model theory holds no guarantee of unambiguous models.

Victor Morgante
5 min readMar 17


Greater Object-Role Modeling mapped to sentences of a theory of finite-model theory. Image by author.

In an earlier article we explored why certain graphical models of Object-Role Modeling can be ambiguous and where for any semblance of formalism to be attributable to Object-Role Modeling (ORM), models under ORM need to be seen in the greater context of the natural language verbalisations that may be derived from the ORM model stored in its entirety within a data structure defined by the metamodel of ORM, and as made available by computer software.

I.e. Only a ‘Greater’ Object-Role Modeling extended beyond the graphical notation of ORM diagrams has any semblance of being able to be considered formal in a logical sense. We draw the triumvirate of the greater Object-Role Modeling, as:

The three essential components of a formal greater Object-Role Modeling. Image by author.

The three essential ingredients of greater Object-Role Modeling are:

  1. ORM diagrams;
  2. Natural language verbalisations of elements of the model expressed in ORM;
  3. The ORM model stored within a data structure expressed by the ORM metamodel, and software to tie graphical ORM models to verbalisations and numbering/highlighting of Join Paths in Join Subset Constraints etc.

Once we have the essential components capable of expressing an Object-Role Model as theorems of a theory of finite-model theory (for example), we can go ahead and do that:

Part of the theoretical set of sentences of a theory under finite-model theory, homomorphic with an ORM model. Image by author.

Generalised Result

If we assume a generalised result…that any ORM model expressed in the greater Object-Role Modeling can be mapped to sentences of a theory under finite-model theory, then we arrive at the modern day interpretation of Object-Role Modeling, of which there is no current proof of any such generalised result. I.e. Dr Terry Halpin’s PhD thesis applies…



Victor Morgante

@FactEngine_AI. Manager, Architect, Data Scientist, Researcher at www.factengine.ai