Entailment 함의

[Dio Jin 교수]

Entailment

1.  An entailment is a proposition (expressed in a sentence) that follows necessarily from another sentence.

e.g. Martina aced chemistry entails Martina passed chemistry, because one cannot ace chemistry without passing chemistry.

2.  Our example sentences pass both tests.
First, the truth of sentence (a) ensures the truth of sentence (b).
If Martina aced chemistry, she necessarily passed chemistry.
Second, the falsity of sentence (b) ensures the falsity of sentence (a).
If Martina didn't pass chemistry, she necessarily didn't ace chemistry.

3. The relation of entailment is unidirectional.

① the opposite order: (b) Martina passed chemistry and (a) Martina aced chemistry.

In this case, sentence (b) does not entail (a)

(if Martina passed chemistry, she did not necessarily ace chemistry-she may have made a C);

② the falsity of (a) does not ensure the falsity of (b)

(if Martina did not ace chemistry, it is not necessarily the case

that she did not pass chemistry-she may, once again, have made a C).

4. There can be a pair of sentences such that each entails the other.

When such a relation holds, it is called paraphrase.

e.g. Martina passed chemistry and What Martina passed was chemistry are paraphrases of each other.

Note, incidentally, that entailment describes the same relationship between sentences that hyponymy describes between words. Likewise, paraphrase describes the same relationship between sentences that synonymy describes between words.

참고: Composite Truth Table for Entailment
P entails Q when the truth of P guarantees the truth of Q,

and the falsity of Q guarantees the falsity of P.

P -----> Q
---------------------
T → T
F → T or F
F ← F
T or F ← T