 These odd results do not arise in some non-classical logics where it is required that premisses be relevant to the conclusions drawn from them, and that the antecedents of true conditionals are likewise relevant to the consequents. But even in those versions of relevance logic which avoid some of these odd results, it is difficult to avoid all of the so-called “paradoxes of implication”(see the entry on  the logic of conditionals  and  relevance logic).  For example, a contradiction (a statement of the form “p and not p”) will be a sufficient condition for the truth of any statement unless the semantics for the logic in question allow the inclusion of inconsistent worlds. 