Assignment

Due on Wednesday, October 29th.

Part 1

In the following exercise, I will describe the behavior of an expression in English—that is, what it can combine with, and what it makes as a result. Based on my description, 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. You can use either the usual notation or the “tree” notation for semantic types in this part.

This expression takes a transitive verb to its left, and then a noun phrase to its left, to form a sentence.
This expression combines with a preposition to its right, and then a verb phrase to its left, to form a transitive verb.
This expression combines with an expression $X$ to its right, where $X$ is something that takes a preposition on its left to form a verb phrase, and together with $X$, it forms a preposition.

Part 2

Recall that in A first approximation of English of the Models module, we assigned the connective and the category $con$ in order to account for sentences like (1).

Ziggy runs and jumps.

Provide a new lexical entry for and that uses the syntactic category system defined in Syntactic categories. Provide lexical entries for runs and jumps (including their meanings), and give a derivation of the sentence in (1).

Part 3

Consider the following sentence, which features an adjective in predicate position.

Ziggy is fast.

Assume that there is a new base category for adjective phrases—call it $ap$—which is the syntactic category of the adjective fast.

What semantic type do you think this category should be associated with? Keep in mind that this semantic type doesn’t have to be $e$ or $t$—it can be something more complex!

What syntactic category should the copula is have? Given this syntactic category, what is the semantic type of is?

--- title: "Assignment" bibliography: ../../semantics.bib format: html: css: ../styles.css html-math-method: mathjax mathjax-config: loader: {load: ['[tex]/bussproofs','[tex]/bbox','[tex]/colorbox']} tex: packages: {'[+]': ['bussproofs','bbox','colorbox']} --- ::: {.hidden} $$ \newcommand{\expr}[3]{\begin{array}{c} #1 \\ \bbox[lightblue,5px]{#2} \end{array} ⊢ #3} \newcommand{\ct}[1]{\bbox[font-size: 0.8em]{\mathsf{#1}}} \newcommand{\abbr}[1]{\bbox[transform: scale(0.95)]{\mathtt{#1}}} \def\true{\ct{T}} \def\false{\ct{F}} $$ ::: Due on Wednesday, October 29th. ### Part 1 In the following exercise, I will describe the behavior of an expression in English---that is, what it can combine with, and what it makes as a result. Based on my description, 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](syn_types.html). You can use either the usual notation or the "tree" notation for semantic types in this part. (1) This expression takes a transitive verb to its left, and then a noun phrase to its left, to form a sentence. (2) This expression combines with a preposition to its right, and then a verb phrase to its left, to form a transitive verb. (3) This expression combines with an expression $X$ to its right, where $X$ is something that takes a preposition on its left to form a verb phrase, and together with $X$, it forms a preposition. ### Part 2 Recall that in [A first approximation of English](../models/english.html) of the Models module, we assigned the connective *and* the category $con$ in order to account for sentences like (@ex-and). (@ex-and) Ziggy runs and jumps. Provide a new lexical entry for *and* that uses the syntactic category system defined in [Syntactic categories](syn_types.html). Provide lexical entries for *runs* and *jumps* (including their meanings), and give a derivation of the sentence in (@ex-and). ### Part 3 Consider the following sentence, which features an adjective in predicate position. (@ex-fast) Ziggy is fast. Assume that there is a new base category for adjective phrases---call it $ap$---which is the syntactic category of the adjective *fast*. What semantic type do you think this category should be associated with? Keep in mind that this semantic type doesn't have to be $e$ or $t$---it can be something more complex! What syntactic category should the copula *is* have? Given this syntactic category, what is the semantic type of *is*?