Igor,
Before commenting on OWL + SWRL, I'd like to say a bit about my qualifications for evaluating hardware and software design. I admit that in my 30 years at IBM, I did quite a bit of research. But I also worked with the IBM large systems development groups, where I learned how computer systems are designed and developed from the circuit level to the mainframe level to the operating system level to the user application level.
First, I suggest a cartoon, which was drawn by one of my colleagues at IBM in 1974: The Adventures of Task-Force Tim,
http://www.jfsowa.com/computer/tftim.htm . The topic is the failure of IBM's huge project called Future Systems (FS). It collapsed in 1974, and high-level management attempted to cover up the failure and salvage something from it.
On a more serious note, see the page on Computer Systems, in which I discuss some lessons learned from those days and from later developments in the computer industry:
http://www.jfsowa.com/computer/ . The first topic is about issues related to FS, including my Memo 125, which was circulated by copying machines throughout IBM. The people who read it loved it (most of them) or hated it (the managers who were responsible). Fortunately, Carl Conti protected me by getting me transferred to the IBM Systems Research Institute, which was outside the chain of command of the people who caused FS and its downfall. That is where I did my research, writing, and teaching about AI, natural language processing, experts systems, and applications to computer software.
And note, by the way, I have been writing critical articles about bad system designs for many years -- even when it got me in a lot of trouble -- plus a lot of praise by people who had been too timid to admit publicly that the design was bad. They didn't have to criticize FS themselves. They just asked someone "Did you see Sowa's Memo 125?" Then depending on the answer, they knew whether it was safe to add their own criticisms.
Since OWL + SWRL have been forced upon innocent victims for almost 20 years, there is a huge amount of legacy software built on top of them. That software is not going away. I am not suggesting that anybody should throw away programs that they have been using for many years. The effects of legacy software don't go away. Everything that follows has to have interfaces to it for many, many years.
But what I am saying is that OWL was a terrible blunder. It is the kind of mistake that very intelligent researchers who have little or no experience with practical software design tend to make. Please read my Memo 125. The kind of blunders that IBM managers made in 1974 comes from the same motivations as the mistakes made by the designers of OWL.
To answer your question, I'll just say that you or anybody else could write an ontology for addition in FOL much simpler, better, and faster than in OWL + SWRL. In fact, you can Google many publications about how to define addition by axioms stated in FOL. It's simple.
John
From: "Igor Toujilov' via ontolog-forum" <ontolog-forum@googlegroups.com>
John,
I hoped you would show us a computer-executable example of how to sum a set of numbers in an ontology, using a publicly available free tool based on FOL or CL.
Igor
Igor,
My recommendation is to replace OWL + SWRL with (1) a simple type hierarchy, equivalent to just the hierarchy part of OWL, which is the most widely used subset, and (2) full first-order logic (FOL) for the constraints.
The requirement of decidability makes the OWL notation (Turtle or whatever) more complex than it should be. That makes it harder to learn, harder to use, and less expressive. And it serves no useful purpose whatsoever. Nobody but a logician who had advanced training could ever write a statement that is undecidable. The Cyc developers, for example, use a superset of FOL, but in 30 years of applications, nobody had ever written an ontology that contained any undecidable statements.
For the type hierarchy, I recommend the four sentence types of Aristotle's syllogisms. Full FOL can be expressed in a very readable and writable notation that uses logical operators with the following spelling: AND, OR, NOT, IF-THEN, SOME, EVERY.
For a summary, see slides 25 to 37 of https://jfsowa.com/talks/patolog1.pdf . That's all you need to express (1) a type hierarchy equivalent to the OWL hierarchy, and (2) constraints in full FOL.
SWRL has some non-logical features, but they are unnecessary if you have full FOL.
This is a simple subset of Common Logic. You can use any standard dialect of CL for the internal representation, and you can use highly readable versions of Controlled English, Russian, or whatever for the user interface.
John