Probably a good idea to read Sheffer stroke - Wikipedia, the free encyclopedia. Also, note that it is non-associative. Good to have your mind that a|b=(not (a and b))
Hmmpf, this is far from straightforward; Use web-searching powers and pen and paper, why are.these true: (is just using the tables i guess.)
(not A) = A | A,
(A and B) = (A | B) | (A | B),
(A or B) = (A | A) | (B | B),
(A if then B) = A | (B | B) = A | (A | B).
Last one is not very clear to me yet. (only if it equals true)
And also. what does the axiom mean here: (U|(U|(V|(U|U)))); (U|(U|(if V then U)))=(if U then (if V then U)) huh? (used the last one given by wikipedia.

Also, I read somewhere that logic can also be based on sets (although that book didnt really go into that :/) Perhaps i will try see if i can find something about it.
Furthermore, In http://socialdiscussion.com/religion....html#post9679, the link Impossible Things for Breakfast given in that post, note that discussing about that is maybe offtopic, as it is not logic as we use. Also, I doubt any of us knows shit about it.(yet)