Axioms for the stronger logics are as follows:
EW is TW plus ((A -> A) -> B) -> B
C is TW plus A -> ((A -> B) -> B)
T is TW plus (A -> (A -> B)) -> (A -> B)
and (A -> ~A) -> ~A
E is T plus ((A -> A) -> B) -> B
R is C plus (A -> (A -> B)) -> (A -> B)
CK is C plus A -> (B -> A)
S4 is E plus A -> (B -> B)
Axiomatisations of fragments of these logics result by
selecting the axioms and rules which explicitly mention
the appropriate connectives.