I have a homework assignment that I am a little stumped on, the questions is:
Describe a sound and complete proof system (axioms and proof rules) for proposition logic. Explain in detail why you believe your proof system is sound and complete. Is your proof system terminating? If yes, explain why. If no, explain why not?
I am stumped for two reasons:
1) I can't seem to find an example of a "sound and complete proof system" my thinking here is that for a proof system to be useful it needs to be both sound and complete, so proof systems dont seem to bother to "state" that they are such.
2) When I asked the lecturer about the assignment, he said that we had discussed two proof systems in class that could be used. The only topics discussed seem to be proof by contradiction and proof by induction, however - I can't seem to find any reference as to what the axioms of these two are. For example, is the only axiom of proof by contradiction that: if $\bot \lnot A$ then $\top A$?
I'd appreciate any help/direction in this.