Sentence Meaning and Natural Language Inference › Presupposition, Implicature, and Other Meaning Layers

Before judging an NLI prediction, identify the meaning relation in the example. Presupposition, conversational implicature, and asserted entailment behave differently, even when an annotation scheme represents them with the same output label.

A presupposition is a background assumption that a sentence takes for granted. It is not the main assertion. When you say "The king of France is bald," the main claim is about the king's hair, but the sentence also quietly assumes that there is a king of France at all. Classic triggers include:

• Definite descriptions: "The king of France" presupposes that there is a king of France.
• Factive verbs: "John knows that the earth is round" presupposes that the earth is round.
• Aspectual verbs: "John stopped smoking" presupposes that John used to smoke.
• Cleft constructions: "It was Mary who broke the vase" presupposes that someone broke the vase.
• Possessives: "Alice's car" backgrounds a salient car associated with Alice; the association need not be ownership.
• Questions: in an ordinary information-seeking use, "Why did John leave?" normally treats John's leaving as given. Such inferences depend on context, and whether they are semantic presuppositions is debated.

In these ordinary readings, the backgrounded content is presented as already available rather than as the main assertion. A listener can still challenge it directly: "There is no king of France." Backgrounding is not immunity from correction.

A useful diagnostic for presupposition is projection: the background inference often survives negation, questioning, and modal embedding. Projection depends on context and embedding structure; it is not an exceptionless rule. This is what distinguishes it from ordinary assertion content, which flips under negation.

If $p$ entails $h$, then $\neg p$ does not generally entail $h$. For example, denying that a poodle barked does not settle whether a dog barked. By contrast, a prior-smoking presupposition often remains available in an ordinary reading of "John did not stop smoking." This projection diagnostic depends on context and embedding. Neither universal cancellation of entailment nor exceptionless projection follows: a tautology, for instance, is entailed by both $p$ and $\neg p$.

Presupposition failure occurs when a required background assumption is not satisfied. If there is no king of France, "The king of France is bald" creates a reference problem. In a Strawsonian analysis, a use of that sentence can fail to make a true or false assertion; this is a theory-specific analysis, not an uncontested treatment of every definite description. The standard three-way NLI alphabet has no separate presupposition-failure label. Annotation instructions therefore need to state how such cases are handled.

This matters in practice. If a document says "The company's new CEO announced layoffs," a reader infers that the company has a new CEO. A question-answering system that ignores this presupposition may miss the existence claim. A factuality evaluation must state whether its support standard covers asserted and presupposed content. Presupposing a proposition does not make it exempt from evidential checking. We will return to presupposition and pragmatics in Part IX.

A conversational implicature is content a speaker conveys beyond what is literally asserted. In Grice's account, listeners use a presumption of cooperation, contextual knowledge, and expectations about informativeness, truthfulness, relevance, and clarity. The scalar examples below concern conversational implicature; conventional implicatures have different properties.

• "Some students passed the exam" often implicates "Not all students passed." The speaker could have said "all," and the choice of the weaker term suggests the stronger one is not warranted.
• "John has at least three children" is compatible with four. Bare numerals such as "John has three children" have competing semantic analyses, so an exactly-three judgment needs an explicit interpretation.

Conversational implicatures are typically cancellable. You can cancel an implicature without contradiction:

Some students passed the exam. In fact, all of them did.

That sounds fine. The implicature is defeated, but the sentence remains coherent. By contrast, you cannot cancel an entailment in the same way. If "A poodle barked" entails "A dog barked," then saying "A poodle barked, but no dog barked" is contradictory. The contrast between cancellable implicature and non-cancellable entailment is one of the sharpest tests we have for distinguishing the two.

Under a strict truth-conditional annotation policy, conversational implicatures should not be treated as entailments. "Some students passed" does not entail "Not all students passed" in strict semantics. An annotation policy must say whether to include that pragmatic enrichment. Otherwise, a disagreement about the policy can look like a model error. Strict logical independence, defeated implicature, and missing context are different reasons a pair might receive a non-entailment label.

Some entailments come from word meaning rather than sentence structure. In the previous chapter on lexical semantics, we saw relations such as hyponymy, hypernymy, synonymy, and antonymy. These relations drive many NLI judgments.

• Hyponymy: "poodle" is a hyponym of "dog." "A poodle barked" entails "A dog barked."
• Hypernymy: "vehicle" is a hypernym of "car." "Alice bought a car" entails "Alice bought a vehicle."
• Antonymy: "open" and "closed" are antonyms in the relevant sense. "The door is open" contradicts "The door is closed."
• Meronymy: "finger" is a part of "hand." "The finger was cut" does not straightforwardly entail "The hand was cut," but it often supports a plausible inference. This is a case where strict entailment and defeasible inference diverge.

Event structure adds another layer. Verbs describe events with participants and roles. "Alice sold Bob a car" entails "Bob bought a car from Alice" because selling and buying are two perspectives on the same transfer event. "Alice gave Bob a book" entails "Bob received a book." "The ice melted" entails "The ice became liquid." These are lexical entailments that depend on the internal structure of the event, not just on set inclusion between nouns. The relation between "sell" and "buy" is not a hypernym relation; it is a relation between two ways of describing a single transaction from opposite viewpoints.

This is a bridge to the next chapter on semantic roles and argument structure. For now, notice that NLI is not only about logic. It is also about lexical semantics, event structure, and world knowledge. A model that masters the logic of "and" and "not" but never learns that selling entails buying will still miss a large and important class of inferences.

Coordination creates entailments that are easy to get wrong. Compare:

• "Alice and Bob left." This entails "Alice left" and "Bob left." The predicate distributes over the conjunction, because leaving is something each person does individually.
• "Alice and Bob lifted the piano." On its collective reading, this does not entail "Alice lifted the piano alone" or "Bob lifted the piano alone." The piano may require their combined effort. An individual can still participate in the joint lift.

The same surface form, "Alice and Bob [verb]ed," supports different inferences depending on the predicate. Some predicates are distributive, some are collective, and some permit either reading in context. Treating every coordinated subject as distributive licenses inferences that the collective reading does not support. Lexical predicate properties and sentence structure both matter.