Questions: Compositional Semantics

Question 1

Which pair of sentences best illustrates the entailment relation?

• A. 'The cat slept on the mat' and 'The cat was on the mat' — the first entails the second
• B. 'It is raining' and 'The streets are wet' — the first entails the second
• C. 'John stopped smoking' and 'John used to smoke' — neither entails the other
• D. 'Every student passed' and 'Some students passed' — the second entails the first

Answer: (A)

Entailment is a strictly logical relation: A entails B when B must be true in every situation where A is true, purely in virtue of meaning. 'The cat slept on the mat' entails 'The cat was on the mat' because sleeping somewhere guarantees being there. Option B fails because streets being wet has independent causes; option D has the entailment direction reversed — 'Every student passed' entails 'Some students passed', not the other way around.

Question 2

Negating a sentence cancels its presuppositions, just as it cancels its ordinary assertions.

• T. True
• F. False

Answer: False

This is the defining property of presuppositions: they survive negation. 'John stopped smoking' asserts he has stopped, but presupposes he was smoking before. The negation 'John didn't stop smoking' cancels the assertion but preserves the presupposition — we still take it for granted that John was smoking. Ordinary entailments and assertions, by contrast, are cancelled by negation.

Question 3

What is scope ambiguity, and why does it arise in sentences with quantifiers?

Model answer: Scope ambiguity occurs when a sentence with multiple quantifiers or operators (like 'every', 'some', or negation) can be interpreted in more than one way depending on which expression takes wider scope. For example, 'Every linguist speaks some language' can mean either that there is one particular language all linguists share (wide scope for 'some') or that each linguist speaks at least one language, possibly different ones (narrow scope for 'some'). It arises because syntax does not always uniquely determine the logical relationship between quantifiers.

Compositionality pairs with syntactic structure, but quantifiers can take scope independently of their surface position. Formal semantic frameworks (like lambda calculus or quantifier raising) make these interpretations explicit by assigning each quantifier a logical scope domain. Understanding scope ambiguity is essential for modeling the full range of meanings a sentence can express.