Questions: Semantic Types and Compositional Meaning

Question 1

A common noun like 'runs' denotes a property — a function that takes an individual and returns a truth value. What semantic type does 'runs' have?

• A. t
• B. e
• C. ⟨e,t⟩
• D. ⟨t,t⟩

Answer: (C)

⟨e,t⟩ is the type of a function from individuals (type e) to truth values (type t). 'Runs' takes an entity — say, Maria — and returns true or false depending on whether that entity runs. This is the canonical type for one-place predicates.

Question 2

A quantifier phrase like 'nearly every student' has the same semantic type as a simple predicate like 'runs', namely ⟨e,t⟩.

• T. True
• F. False

Answer: False

Quantifiers are higher-order: they take a property (type ⟨e,t⟩) and return a truth value (type t), giving them type ⟨⟨e,t⟩,t⟩. 'Every student runs' composes by applying the quantifier to the predicate, not by applying a predicate to an entity. Treating quantifiers as type ⟨e,t⟩ would collapse the distinction between predicates and determiners.

Question 3

What role does the type system play in compositional semantics — why does assigning types to expressions matter for computing sentence meanings?

Model answer: Types constrain which expressions can combine: a function of type ⟨σ,τ⟩ can only apply to an argument of type σ, yielding a value of type τ. This prevents meaningless combinations and specifies exactly how meanings compose step by step, making the derivation of sentence meaning fully explicit and mechanically verifiable.

Without types, we could try to combine any two expressions, but many such combinations would be semantically ill-formed (e.g., applying a truth value to another truth value). Types make compositionality precise: each application step is licensed by a type-matching rule, so the system can compute complex meanings — including quantifier scope — in a principled way.