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\noindent
{\bf Homework 2\\
11-721: Grammars and Lexicons, Fall 2008\\
Due Monday, October 6, 2008}


\section{Based on Radford, Exercise XVI, page 225}

\noindent
Assume the following phrase structure rules:

\begin{verbatim}
S --> N''  VP

VP --> V'
VP --> V' PP
V' --> V
V' --> V N''

PP --> P  N''

N'' --> (Det) N'
N' --> N' PP
N' --> N  (PP)

N --> N CONJ N
N' --> N' CONJ N'
N'' --> N'' CONJ N''

Det --> that
Det --> his
Det --> the
CONJ --> and 

V --> like
VP --> just don't get on

N --> picture
N --> pushchair
N --> workers
N --> managers
N --> factory
N'' --> I
N'' --> him
P --> of
P --> in
\end{verbatim}

\newpage

\noindent
{\bf Question 1:} Note that {\it I\/} and {\it him\/} are {\tt N''}
and not N.  Write an ungrammatical sentence that would be generated if
``I'' and ``him'' were N and not NP.  This grammar generates a lot of
ungrammatical sentences, so be sure to write one that is ungrammatical
for the right reason.

%% Why are ``I'' and ``him'' NPs instead of N's?

\noindent
{\bf Question 2:} Note that {\it his\/} is a determiner.  Write an
ungrammatical sentence that would be generated if {\it his\/} were an N.
Write a sentence that could not be generated if {\it his\/} were an NP.

%% Why is ``his'' a Det?

\noindent
{\bf Question 3: Assuming that there is an attachment ambiguity in
{\it that picture of him in his pushchair\/}, what are the two
meanings?} 

\noindent
{\bf Question 4:} The phrase structure rules don't generate a tree
that corresponds to one of the meanings.  Which one is it?

\noindent
{\bf Question 5:} Draw a phrase structure tree for the meaning that is
generated.

\noindent
{\bf Question 6:} There is also an attachment ambiguity in {\it The
workers and the managers in the factory just don't get on\/}.  What
are the two meanings?

\noindent
{\bf Question 7:} The phrase structure rules don't generate a tree
that corresponds to one of the meanings.  Which one is it?

\noindent
{\bf Question 8:} Draw a phrase structure tree for the meaning that is
generated.

\noindent 
{\bf Question 9:} Radford suggests to reformulate the rule that
introduces PP adjuncts into three rules, one for adjuncts to X, one
for adjuncts to X', and one for adjuncts to X''.  Write the new phrase
structure rules.  

\noindent
{\bf Question 10:} Using the new rules, draw a tree for the meaning of
{\it that picture of him in his pushchair\/} that wasn't
previously generated.

\noindent
{\bf Question 11:} Using the new rules, draw a tree for the meaning of
{\it The workers and the managers in the factory just don't get on\/}
that wasn't previously generated.

\section{Possessive Noun Phrases}

In the last problem, possessive pronouns like {\it his\/}
were treated as determiners.  However, possessors can be full noun
phrases as in {\it the boy across the street's toy\/} where the
possessor is {\it the boy across the street\/}.\\[6pt]

\noindent
The {\it 's\/} is a {\it clitic\/}, not a full word, but not a prefix or
suffix.  One of the things that makes it different from prefixes or
suffixes is that it attaches to words that aren't related to it.  In
{\it the boy across the street's toy\/} the {\it 's\/} indicates that
the boy is a possessor, but it attaches to {\it street\/}.
In the phrase structure rules below, the {\it 's\/} is treated as a
terminal symbol that is a daughter of NP.  \\[8pt]

\noindent
{\bf Task 1:} Using the phrase structure rules below, draw two trees
for {\it the wife of your friend's brother\/}, which has two different
meanings.   Assume that {\it of your friend\/} is an argument, not an
adjunct.   For the sake of simplicity, {\it your\/} is still treated
as a determiner because it does not occur with {\it 's\/}. \\[6pt]

\noindent
{\bf Task 2:} Using the phrase structure rules below, draw two trees
for {\it We gave her dog biscuits\/}.  The verb {\it give\/} should
have three arguments: agent, theme, and recipient.\\[6pt]


\begin{verbatim}
S --> N''  VP

VP -->  V  N''  N''  

PP -->  P  N''

N'' --> (Det) N'
N'  -->  N  (PP)
N'' -->  NP  's   N'

In the previous rule, the N'' has three daughters, NP, 's, and N'.  

Det --> the
Det --> your
Det --> her
N'' --> her
N'' --> we

N -->  N   N
\end{verbatim}

\noindent
{\bf Task 3 (Extra Credit, five percent):} When there is an NP
consisting of {\tt NP 's N'}, what principle determines that the N-bar
and not the possessor NP is the head of the whole NP?  I'm looking for
a syntactic principle, which might be found somewhere in Radford's
book.  A semantic principle is reasonable --- {\it the boy's book\/}
is a book, not a boy --- but that is not the answer I'm looking for.
The answer is very specific and pretty short.  

\section{Drawing F-structures}

On the next page there is a lexicon and a reduced set of rules in LFG
notation.  Draw the f-structures for the two readings of {\it the
friend of your wife's brother\/}.\\[6pt]

\newpage
\begin{tabular}{llccc}
%% S & $\rightarrow$ &   N$''$ &   VP & \\
%% & & ($\uparrow$ {\sc subj})=$\downarrow$ & $\uparrow = \downarrow$\\
%%
%% & & & & \\
%% & & & & \\
%%
%% VP & $\rightarrow$ &  V &  N$''$ &  N$''$ \\
%% & & $\uparrow = \downarrow$ & ($\uparrow$ {\sc obj})=$\downarrow$ & ($\uparrow$ {\sc obj2})=$\downarrow$\\
%% 
%% & & & & \\
%% & & & & \\

PP  & $\rightarrow$ &  P  & N$''$ \\
& & $\uparrow = \downarrow$ & $\uparrow = \downarrow$ & \\

& & & & \\
& & & & \\

N$''$ & $\rightarrow$ &  (Det) & N$'$ \\
& & $\uparrow = \downarrow$ & $\uparrow = \downarrow$ & \\

& & & & \\
& & & & \\

N$''$ & $\rightarrow$ &  (Det) & N$'$ \\
& & ($\uparrow$  {\sc poss})= $\downarrow$ & $\uparrow = \downarrow$ & \\
& & ($\downarrow$  {\sc pron})=c $+$ \\

& & & & \\
& & & & \\

N$'$ & $\rightarrow$ & N & (PP)\\
& & $\uparrow = \downarrow$ & ($\uparrow$ {\sc obl}-poss) = $\downarrow$ & \\

& & & & \\
& & & & \\

N$''$ & $\rightarrow$ & N$''$ & $'$s & N$'$\\
& & ($\uparrow$  {\sc POSS}) = $\downarrow$ & & $\uparrow = \downarrow$  \\

\end{tabular}

\vspace{24pt}


\begin{tabular}{lll}
{\it the} & {\sc det} & ($\uparrow$ {\sc def}) = $+$\\
& & \\
{\it wife\/} & {\sc n} & ($\uparrow$ {\sc pred}) = $'$wife$'$\\
& & \\
{\it of} & P\\
& & \\
{\it your} & det & ($\uparrow$ {\sc pred}) = $'$pro$'$\\
& & ($\uparrow$ {\sc num}) = sg\\
& & ($\uparrow$ {\sc pers}) = 2\\
& & ($\uparrow$ {\sc pron}) = $+$\\
& & \\
{\it friend\/} & {\sc n} & ($\uparrow$ {\sc pred}) = $'$friend$'$\\
& & \\
{\it brother\/} & {\sc n} & ($\uparrow$ {\sc pred}) = $'$brother$'$\\
\end{tabular}


\end{document}

