The logical link between conjunction and implication is provided by something as fundamental as the inference rule modus ponens formula_45: from formula_5 and formula_47 follows formula_6. In the fuzzy logic case that is more rigorously written as formula_49, because this makes explicit that our confidence for the premise(s) here is that in formula_50, not those in formula_5 and formula_47 separately. So if formula_26 and formula_28 are our confidences in formula_5 and formula_6 respectively, then formula_57 is the sought confidence in formula_47, and formula_59 is the combined confidence in formula_50. We require that