Hi! I'm a high school student and I've been interested in Logic for some time... Although I read some books and acquired some knowledge, I still have one question that remains unanswered in spite of my hard work... My tutor told me that the three axioms of Propositional Logic (see them for example at http://en.wikipedia.org/wiki/Axioms) were chosen independently from the (semantic) meaning of the "implication" connectives and thus independently from the number of truth values (true/false; 0/0.5/1 and so on)... Is it true? I didn't understand his explanation and so I began my own study of this subject. Does anyone of you know any Internet source or a book that deals with the choice of axioms of Propositional Logic in detail? Thanks a million!