I have an Primal Integer Linear Program where in some constraints there is a combination of two 0-1 decision variables say $A[u,x]$ and $B[u,v,x,y]$ (the indices here are not necessaray to be the same) in the form of "if then constraint" that handles some special cases of my problem. One constraint looks like this: $$ for (u,v) \in A: for (x,y) \in E : A[u,x] + A[v,y] <=B[u,v,x,y]+1 .(I) $$
I would like to construct the Dual ILP and being not expert in Linear Programming I am wondering if in the Dual I have to take care of the meaning of constraint and keep the same behaviour as in the Primal? In other words, do I have to come up with a constraint doing the same job in the Dual as in the Primal?
Grateful to any suggestions and clarifications.