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Entailment is a situation in which the truth of a given sentence necessitates the truth of some related sentence. If the sentence Susan is taller than Jane is true, then we know for sure that the sentence Jane is shorter than Susan is also true. These two sentences mutually entail each other. Similarly, if the active sentence Frank bought a green bicycle is true, then we know for sure that the passive counterpart A green bicycle was bought by Frank is also true. We again have mutual entailment.

Often entailment points in one direction only. If the sentence Susan eats carrots and turnips is true, then the sentence Susan eats vegetables is also necessarily true. In this case, however, entailment is not mutual, for the truth of the sentence Susan eats vegetables does not entail the truth of the sentence Susan eats carrots and turnips.

My question has to do with entailment of the latter sort, i.e. the type that points in one direction only. Does a sentence with an adjunct entail the same sentence without the adjunct? For instance, does the truth of sentence (1) entail the truth of sentence (2)?

(1) Frank arrived on Friday.

(2) Frank arrived.

Intuitively, my answer in this case is “Yes, it does”. But now consider the next two sentences:

(3) Frank called the woman in his class.

(4) Frank called the woman.

In this case, intuition fails me. I am unsure whether the truth of sentence (3) entails the truth of sentence (4). Sentence (4) seems vague in such a way that does not allow one to reach a conclusion about potential entailment, one way or the other. Note that on Friday in (1) is an adjunct on the verb arrived, whereas in his class in (3) is an adjunct on the noun woman.

So, how should we understand the influence of adjuncts on entailment patterns?

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    It's the use of the and the presuppositions involved in definite descriptions that's failed you. Entailment is largely a matter of individual lexical items rather than structures; since "adjunct" is a wastebasket category its presence or absence shouldn't have anything to do with entailment.
    – jlawler
    Aug 23 at 16:02
  • If P entails Q, that does not entail that "not P" entails "not Q" (in fact not Q entails not P). "I never eat meat for breakfast." does not entail "I never eat meat."
    – Rosie F
    Aug 23 at 16:23
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    Sentences are about linguistics and they are mere structures. It's statements that entail things and statements are about logic. Your question is about logic, and entailment has nothing to do with particular sentence structures, it works in all the languages irrespective of which sentence structure the given statement takes in the given language.
    – Yellow Sky
    Aug 23 at 17:53
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Considering that adjuncts are considered pieces of sentences that add additional information about time, place, manner etc. without changing the core meaning of the sentence, yes, it makes sense that a sentence with an adjunct would entail the sentence without the adjunct.

This is especially visible in event semantics, where the semantic content of an adjunct is typically conjoined (and-ed) with the phrase it combines with:

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The semantics of the VP together with the adjunct reads "is an event which is a buttering event and whose theme is the toast and which is a slow event".

Since a conjunction always entails each of its conjuncts (A and B always entails A and entails B), a semantic representation where an adjunct is added via conjunction always entails the sentence without the conjoined adjunct:

∃e. Butter(e) ^ agent(e) = john ^ theme(e) = thetoast ^ Slow(e)

∃e. Butter(e) ^ agent(e) = john ^ theme(e) = thetoast

It would work the same way with PP adjuncts, e.g.

(1) ∃e. Arrive(e) ^ theme(e) = frank ^ time(e) = friday

(2) ∃e. Arrive(e) ^ theme(e) = frank

(3) ∃e. Call(e) ^ agent(e) = frank ^ theme(e) = thewoman ^ In-class(thewoman,frank)

(4) ∃e. Call(e) ^ agent(e) = frank ^ theme(e) = thewoman

The last sentence one could perhaps analyze in more detail and say that "the woman in his class" denotes the unique individual such that they is a woman and in class with Frank, and "the woman" without the adjunct may fail to denote since there may be no unique woman, in which case the sentence would have no or a false truth value and the entailment fails.

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