Entailment is a centrally important type of inference in semantics. While the pragmatic inferences called explicatures and implicatures are cancellable, an entailment is a guarantee.

Using the notation ⇒ for entailment, (1.19a) indicates that when The accommodation was excellent is true, we can be sure that it (the same accommodation at the same point in time) was very good. The statement in (1.19b) signifies that if it was excellent, it was (at least) good; and (1.19c) signifies that it was (at least) OK.

Strictly speaking, entailment holds between propositions. However, explicated utterances based on declarative sentences express propositions and no great harm will come from the shortcut of thinking about a sentence as entailing other sentences (provided each sentence is considered in just one of its meanings, which amounts to it being an explicated utterance.

Contrast the cancellability of the ‘not all that good’ guess that A made in (1.5) with the certainty of the inferences in (1.19).

The examples in (1.20) illustrate further points about entailment:

When (1.20a) is true we can be sure that (1.20b) is also true (provided it is the same Moira and the same city). This is shown in (1.20c) as a statement about entailment. Attempting to cancel an entailment leads to contradiction, as in (1.20d). If the first clause in (1.20d) is true, it entails the proposition expressed by a non-negative version of the and … clause. Tacking on the negative clause yields a contradiction.

Examples (1.21a, b) show other entailments of (1.20a).

The word arrived is an important contributor to (1.20a) having the entailments shown. For instance, if lived or been were substituted for arrived, the entailments would be different. If someone not fully proficient in English asks what arrive, means, a sentence like (1.20a) could be given as an example, explaining that it means that Moira journeyed from somewhere else (Birmingham perhaps) and is now in Edinburgh. (The construction with has in (1.20a), called present perfect in grammar books, is crucial to the entailment in (1.20c)

If (1.20a) is understood and accepted as true, then none of the entailments in (1.20c) and (1.21a, b) needs to be put into words. They follow if (1.20a) is true; they can be inferred from it; they derive from the meaning of arrive. It would be fair to say that the main point of choosing which words to use when talking or writing is to select among entailments. The sense of a word can now be defined in terms of the particular entailment possibilities that sentences get from containing that word: whatever aspects of the word’s meaning are responsible for the sentences having those entailments are its sense.

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