Challenge 2025: Strict Forest for Relevant Logic

Hi,
Ok, I am an ornithologe that is mainly
interested in strict forests , where there
are no mocking birds, since everything
is simple typed. Now among the strict forests,
are certain forests that follow a multi-valued
logic. Basically each bird group is a law of a
multi-valued logic. Like for example these bird
groups, the type parameters are given in curly brakets:
I{X} : (X -> X)
B{X,Y,Z} : ((Y -> Z) -> ((X -> Y) -> (X -> Z)))
C{X,Y,Z} : ((X -> (Y -> Z)) -> (Y -> (X -> Z))))
S{X,Y,Z} : ((X -> (Y -> Z)) -> ((X -> Y) -> (X -> Z)))
K{X,Y} : (X -> (Y -> X))
W{X,Y} : ((X -> (X -> Y)) -> (X -> Y))
Here is an example multi-valued logic, Łukasiewicz
three valued logic, that satisfies B, C and K, but not W:
(0->0)=2 (0->1)=2 (0->2)=2
(1->0)=1 (1->1)=2 (1->2)=2
(2->0)=0 (2->1)=1 (2->2)=2
Is there a multi-valued ogic, that satisfies S, B, C
and I, but not K?
Bye