Hasse diagram for Four-valued Logic Algebra

Question

For given algebra ({0,1,X,Z}, . , +) which “.” represent “Logical And” and “+” represent “Logical Or”, Following lookup tables are given (image):

I guess the Hasse Diagram of a 4-Valued logic should be something like this (image) :

But, If this is truely Hasse Diagram of 4-valued logic, what is a Right arrengement for X and Z and their complements in this Lattice ?

Answer 1

As @Théophile mentioned, It seems there is no difference between X and Z , So X=Z and we have a 3-valued Logic and It’s Hasse Diagram shape a Chain graph, as you can see in this image:

And it’s Relation could be this:

R={(0,x),(0,1),(x,1),(0,0),(x,x),(1,1)}

P.S. However complements are not match with this Hasse diagram. i think multi-valued logic like this one, which i don’t know is a 3-value logic or not, could have another Hasse diagram which i don’t know. Please if anyone has a better answer share it with me, Thanks.