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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.