In the following number of posts I will give a brief overview of a mathematical formalization of object orientation. Rather than boring you with the mathematical details I will give an intuitive understanding of the formalization by providing illustrative examples. If you are keen on diving into the mathematical details, you are welcome to consult Scenario Testing Using OWL.

Here is a reading list to guide you:

1. First, let us recall some basic OO theory.
2. The mathematical formalization I will use here is based on Description Logics (DLs).
3. There is an intuitive correspondence between OO and DLs.
4. Let us look at an example of a simple class.
5. Let us add some more attributes to our class.
6. A brief introduction to Protege and reasoners.
7. Now on to class inheritance!
8. Here is how we deal with associations between classes.

If have any related questions you are most welcome to leave a comment with your question.