In this work, we study a recent extension to the well-known Steiner tree problem: the Generalized Group Steiner Tree problem with logical side constraints. In this variant, we aim to identify a tree of minimum total cost, that spans a given set of groups of nodes, like in the traditional Group Steiner Tree problem. However, these groups are now subject to logical relationships that either allow or disallow their immediate presence in the tree. The logical constraints that we investigate here include AND, OR, XOR, XNOR, NAND, and IF/THEN (implication) relationships between the groups. We provide mathematical formulations for this variant of the Generalized Group Steiner Tree problem for each of the possible logical relationship side-constraints. We also present a numerical experiment to showcase the increased computational effort required to solve this variant, as opposed to its traditional Group Steiner Tree counterpart. Our experiments reveal that implication (IF/THEN) constraints appear to be the most difficult to incorporate. We conclude the work with a summary of our contribution and findings, and report possible avenues for future exploration.