Assignment

Due on Wednesday, November 5th.

Part 1

This exercise is basically just like Part 1 of the previous assignment. I want you to have a chance to practice a bit more figuring out what syntactic category and semantic type something has, based on a description of its distribution. Importantly, none of the expression behaviors I will describe here necessarily correspond to anything you actually see in English or any other language. The point of the exercise is for you to get comfortable translating the informal description in English into a formal description of an expression’s syntactic category and semantic type.

Again, I will describe the behavior of an expression in English—what it can combine with, and what it makes as a result—and again, I want you to:

  • say what its syntactic category is in “parentheses” notation;
  • say what its syntactic category is in “tree” notation;
  • say what its semantic type is, assuming the category-type correspondence discussed in Syntactic categories of the previous module. As before, you can use either the usual notation or the “tree” notation for semantic types here.

  1. This expression takes a preposition to its left, and then a ditransitive verb to its right, to form a noun phrase.

  2. This expression combines with a coordinator of verb phrases to its right (e.g., and), and then a preposition to its left, to form a sentence.

  3. This expression combines with an expression \(X\) to its left, where \(X\) is something that takes a coordinator of sentences on its left to form a verb phrase, and together with \(X\), it forms a preposition.

Part 2

English has a syntactic voice distinction between active verbs and passive verbs. This means that in addition to sentences like (1), where we see the transitive verb ate,

  1. Tigress ate noodles.

it is also possible to form sentences like (2), in which the very same verb has been passivized.

  1. Noodles were eaten.

To analyze sentences with passive verbs in them, let’s assume that we have another base syntactic category:

\[v_{\textit{pass.}}\]

Assume that this base category is associated with the following semantic type:

\[(e → t)\]

Thus semantically, \(v_{\textit{pass.}}\) is just like the syntactic category \((np\backslash s)\) of verb phrases!

Further, let’s assume that ate has the following lexical entry:

\[⟨\textit{ate}, (λx.(λy.\ct{eat}(y, x)))⟩ ⊢ ((np\backslash s)/np)\]

It takes two semantic arguments, one corresponding to the direct object and one corresponding to the subject, and it gives back \(\true\) if the second argument eats the first argument (and it gives back \(\false\), otherwise).

To analyze the passive verb eaten, let’s assume that it has the following lexical entry:

\[⟨\textit{eaten}, (λx.\{y ∣ \ct{eat}(y, x)\} ≠ \varnothing)⟩ ⊢ v_{\textit{pass.}}\]

In words, the interpretation of eaten is a characteristic function of some set of entities. Specifically, it is the characteristic function of the set of entities such that the set of things that eat them is not the empty set.

Provide a lexical entry for the auxiliary verb were that allows you to derive the sentence in (2).

Part 3

Assume, as usual, that Tigress is a noun phrase whose interpretation is \(\ct{ti}\), and that noodles is a noun phrase whose interpretation is \(\ct{n}\). Provide a derivation of the sentence in (1). Use your lexical entry for were to provide a derivation for the sentence in (2). Do the meanings you obtain for the two sentences help explain the fact that (1) entails (2)?