ABSTRACT
There are variants K Jol of the calculi KJ0 which omit the rule (AINA) and, besides the axioms A A , use additional 3-axiom s A = > x (or generali zed J -ax iom s A,M ==$ x in the case of K Jolu). C learly, every K Jol~derivation becomes a KJ0~ derivation if the J-ax iom s are replaced by instances of (AINA).
