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For example, the sentence (A) The president was assassinated. entails (B) The president is dead. Notice also that if (B) is false, then (A) must necessarily be false. To show entailment, we must show that (A) true forces (B) to be true and (B) false forces (A) to be false.
Entailment differs from implicature (in their definitions for pragmatics), where the truth of one (A) suggests the truth of the other (B), but does not require it.[dubious ] For example, the sentence (A) Mary had a baby and (B) got married implicates that (A) she had a baby before (B) the wedding, but this is cancellable by adding -- not necessarily in that order. Entailments are not cancellable.
Entailment also differs from presupposition in that in presupposition, the truth of what one is presupposing is taken for granted. A simple test to differentiate presupposition from entailment is negation. For example, both The king of France is ill and The king of France is not ill presuppose that there is a king of France. However The president was not assassinated no longer entails The president is dead (nor its opposite, as the president could have died in another way). In this case, presupposition remains under negation, but entailment does not.
Types of Entailment
There are three types of entailment: formal or logical entailment, analytic entailment, synthetic entailment.