Implication (pragmatics)

In pragmatics (linguistics), implication is the relationship between two sentences where the truth of one sentence suggests the truth of the other, but--distinguishing implication from entailment--does not require it. For example, the sentence Mary had a baby and got married strongly suggests that Mary had the baby before the wedding, but the sentence would still be strictly true even if Mary had her baby after she got married. Further, if we add the qualification -- not necessarily in that order to the original sentence, then the implication is cancelled even though the meaning of the original sentence is not altered.

This can be contrasted with cases of entailment. For example, The president was assassinated. does not just suggest that The president is dead. is true; it requires it. There is no way that the first sentence could be true without the second sentence being true; if the president weren't dead then whatever happened to him wouldn't have counted as a (successful) assassination. Similarly, unlike implications, entailments cannot be cancelled; there is no qualification that you could add to The president was assassinated which would cause it not to entail The president is dead. while also preserving the meaning of the first sentence.