Alex,

As I have said many times, in email notes, slides, and publications, a precise formal ontology of everything cannot be done until all the unsolved problems in the foundations of every science have been solved.  That includes psychology (of humans and all other living things on any planet in the universe).  

But I do believe that it's possible and highly desirable to develop formal ontologies of things that are implemented on digital computers.  The reason why that's possible is that anything implemented  in strings of bits is discrete and finite.  Therefore the implementation itself is a formal definition of what the program does. And a formal description in a more concise and readable form is possible and valuable..

I am happy to see that you are considering "the field of knowledge itself: education, the learning process, and so on is of course very interesting as a branch of Psychology."   

Nothing in any of those topics can be formalized precisely because every one of them has an enormous number of unknown issues for which the best known studies are incomplete.  I have a high respect for what has been done in those fields.  But every research issue they solve opens up many, many more unsolved problems.

Attempts at formalization can be useful in order to show the vast realm of unknown and unknowable issues that make any formal theories of everything hopeless.  

Re:  " they stopped classifying objectives and moved on to classifying mental abilities themselves."   

That seems to be a step toward  recognizing the immense scope of the problem.    But it's essential to make the distinction between the formal representation of what is computable and the unknown and poorly understood  continuum of the mind and the world.   The discrete can be formalized, but it's impossible to formalize the continuum in any finite notation with a discrete set of symbols.

Engineers have an excellent way of summarizing these issues:  "All theories are wrong, but some are useful."

John