x1 is relevant logic / relevance logic, used to deduce/infer x2 (du'u)
A substructural logic where the antecedent and consequent of implications are constrained to stay "relevant" (srana) to each other. ("Weakening", adding irrelevant truths to the set of antecedents, is not allowed.) See also xaklogji, xakyziflogji, fadylogji, zbalogji.