gee, Johannes, do you mean something of a boolean system? Woha, dude, do you mean the set is closed under the operators? Woha. Geee, nobody ever thought of that before!? Do you think, maybe, one could define axioms of the system and prove the truth of statements in the system? Ohh... Woha dude. What a concept. Gee, I wonder if you can prove, syntactically, the truth of every statement that is semantically true in the system? We cold call that completeness. and....

Give me a break. People have been thinking about foundations for 5000 years. You are completely talking out your behind here. I wrote the interactive online textbook on basic symbolic logic. Implemented it too, and put it on the web.

Davin L.