These 'rules' can be excluded by contrary implication or express agreement. Relevance logic attempts to capture these alternate concepts of implication that material implication glosses over. "Inference" is not to be confused with "implication". See material implication (rule of inference). The former assumes that the operator of implication between two hypotheses produces a hypothesis. British officials were therefore irritated by the implication that sovereignty was negotiable. The archaeology suggests that the literary implication of a deserted city is probably not true. The implication of Laius's oracle is ambiguous. A presupposition is an implication through chosen language. The converse implication and the strong Goldbach conjecture remain unproven. It is also used before a sentence for a sense of implication. An important implication of marginal propensity to save is measurement of the multiplier. The converse implication, however, does not hold. This follows from the implication , which we will now prove. Faustus fails to see them as warnings and ignores their implication.