Ken
A quite interesting essay.
If I understand well your axiomatic system describes the behavior of a "particle" and it's movement in a manner that makes me recall the game of life.
I should study it deeper to make further comments.
But I though I should drop a comment.
As a professional I also am a computer and IT related entrepreneur who has gone back to study physics. For me this is a hubby, if this essay of you is result of your hubby, I guess you've gone a long way with this axiomatic system.
I've been following professor Susskin physics courses via web, essentially because I don't live in the area. I live in Mexico city, but I did live an study at Berkeley and Fremont some many years ago. Currently my company represents SGI in Mexico, so I travel there often.
Please read my essay and drop a comment if you can. In the mean time I will continue studing your essay.
Regards