Sentence Meaning and Natural Language Inference › What Sentence Meaning Adds

Sentence meaning combines word meanings according to their structure. The principle of compositionality makes that relationship explicit.

The key phrase in that principle is "the rules used to combine them." Word meanings alone are not enough, because the same words can be assembled in more than one way. Systematic combination rules help explain how readers interpret sentences they have never encountered as complete expressions. This is one motivation for compositionality, rather than a claim that syntax and a list of literal word meanings account for every contextual interpretation.

Compositionality explains why "The cat chased the dog" and "The dog chased the cat" differ despite sharing the same words. The words contribute entities and relations, while their combination assigns the roles. In "The cat did not chase the dog," negation denies the proposition that the cat chased the dog; it does not replace the dog with a non-dog. The verb phrase describes a property before its subject is supplied. In "The cat chased the dog and the dog chased the cat," the coordinating "and" joins two propositions about the same two animals in reversed roles. Conjunction alone does not determine whether we describe the chasing as separate episodes or parts of one larger event.

A useful way to formalize sentence meaning is through truth conditions. The truth-conditional approach does not ask what a sentence "makes you picture." It asks a sharper question: in which situations would this sentence be true? Let $\mathcal{W}$ be a set of possible situations or worlds. A sentence $s$ denotes a set of worlds:

where:

• $\mathcal{M}(s)$: the set of worlds in which sentence $s$ is true
• $\mathcal{W}$: the set of all possible worlds under consideration
• $\subseteq$: set inclusion, so $\mathcal{M}(s)$ is a subset of $\mathcal{W}$

The set $\mathcal{M}(s)$ contains exactly those worlds in which $s$ is true. This is a simple but useful idea, because it turns meaning into an object we can manipulate with ordinary set operations:

• "The cat is on the mat" denotes the set of worlds where the cat is on the mat.
• "The cat is not on the mat" denotes the complement of that set.
• "The cat is on the mat and the dog is barking" denotes the intersection of two sets.
• "The cat is on the mat or the dog is barking" denotes the union of two sets.
• "Every cat is on a mat" denotes worlds where the set of cats is a subset of the set of things on mats.

In this simplified classical model, each sentence is true or false at every considered world, and "or" is inclusive. Negation is then complement within $\mathcal{W}$, conjunction is intersection, and disjunction is union. Universal quantification can be expressed as inclusion between predicate extensions within a world, as we will see below. Presupposition failures that lack a truth value require a richer semantics; the complement rule does not silently cover those cases.

This truth-conditional view does not capture everything about meaning. It does not directly capture emphasis, sarcasm, social meaning, or the conversational suggestion that "some" can convey "not all." Two sentences can have the same truth conditions yet feel different, as when one is more polite, more emphatic, or more informative. But it gives us a precise core for entailment and contradiction, and that core is enough to make NLI a well-defined task.

Structure is not optional. The sentence "I saw the man with the telescope" has at least two readings:

• I used a telescope to see the man.
• I saw the man associated with or in possession of the telescope.

The words are the same, but the syntactic attachment differs. In the first reading, "with the telescope" describes the instrument of seeing. In the second, it modifies "man," associating the telescope with him. Physical holding is one possible interpretation, not an entailment of noun attachment: his telescope could be mounted on a tripod beside him. The two attachments therefore support different inferences. This is one reason the syntax chapters in Part VII matter for semantics.

Context matters too. "She is here" depends on who "she" refers to and where "here" is. "The meeting is tomorrow" depends on the utterance time. Lexical ambiguity is related but distinct: "bank" has financial and river-edge senses, while the local phrase "raised rates" already selects the financial sense in ordinary literal use. A shorter phrase such as "near the bank" may need more context. Sentence-pair datasets such as SNLI provide much less discourse than a complete conversation or document. Success on isolated pairs need not transfer to passages where pronouns and definite descriptions depend on earlier text. Coreference and discourse relations return in Part IX.

For now, keep three levels separate:

• Sentence meaning: truth conditions and entailment relations. This is what the sentence says once lexical senses, contextual referents, and relevant times have been fixed.
• Speaker meaning: what a speaker intends to convey in context. This includes implicature, irony, emphasis, and all the ways an utterance can mean more than its literal content.
• World knowledge: facts about the actual world that help decide whether a relation holds. Knowing that Paris is in France lets you judge that "The Eiffel Tower is in Paris" entails "The Eiffel Tower is in France," even though nothing in the words themselves encodes that geography.

An NLI judgment can depend on more than one of these levels. Recognizing which level a given example depends on is the first step toward interpreting a model's errors correctly.