Assignment

\[ \newcommand{\expr}[3]{\begin{array}{c} #1 \\ \bbox[lightblue,5px]{#2} \end{array} ⊢ #3} \newcommand{\ct}[1]{\bbox[font-size: 0.8em]{\mathsf{#1}}} \newcommand{\abbr}[1]{\bbox[transform: scale(0.95)]{\mathtt{#1}}} \def\true{\ct{T}} \def\false{\ct{F}} \]

Due on Wednesday, December 3rd.

Part 1

Provide a derivation of the sentence in (1).

1. No fake chair is round.

(Assume that chair is a noun that denotes a characteristic function of some subset of the relevant model’s domain.)

Part 2

Let’s hypothesize, at least for the sake of this exercise that, that only is a quantificational determiner; that is, let’s suppose that its syntactic category is \(((s/(np\backslash s))/n)\). Propose a lexical entry for only, including a meaning.

Part 3

Is the meaning you proposed for only in Part 2 conservative? Show whether it is or isn’t, following the examples given in Conservativity. Make sure that your demonstration is completely general, in the sense that it holds for any two characteristic functions \(f\) and \(g\)!