what is Entailment?

Definition:

In semantics, the principle that under certain conditions the truth of one statement ensures the truth of a second statement.

·  [O]ne statement entails another when the second is a logically necessary consequence of the first, as Alan lives in Toronto entails Alan lives in Canada. Note that the relationship of entailment, unlike that of paraphrase, is one-way: it is not the case that Alan lives in Canada entails Alan lives in Toronto."
(Laurel J. Brinton, The Structure of Modern English: A Linguistic Introduction. John Benjamins, 2000)

·  "[M]any, if not all, assertive sentences (statements, propositions) of a language allow for inferences solely on the basis of their meanings. For example, when I say Ben has been murdered, then anyone who has understood this utterance and accepts its truth will also accept the truth of the statement Ben is dead."
(Pieter A. M. Seuren, Western Linguistics: An Historical Introduction. Wiley-Blackwell, 1998)

·  An entailment can be thought of as a relation between one sentence or set of sentences, the entailing expressions, and another sentence, what is entailed. . . .

We can find countless examples where entailment relations hold between sentences and countless where they do not. The English sentence (14) is normally interpreted so that it entails the sentences in (15) but does not entail those in (16).

(14) Lee kissed Kim passionately.

(15)
a. Lee kissed Kim.
b. Kim was kissed by Lee.
c. Kim was kissed.
d. Lee touched Kim with her lips.

(16)
a. Lee married Kim.
b. Kim kissed Lee.
c. Lee kissed Kim many times.
d. Lee did not kiss Kim.