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\noindent
{\bf Homework 1\\
11-721: Grammars and Lexicons, Fall 2007\\
Due Monday, September 17, 2007}

\section{Predeterminers, Determiners, and Adjectives}

\noindent
In this problem you will examine the distributional and morphological
properties of three parts of speech in English:  predeterminers,
determiners, and adjectives.   This is a realistic exercise:  you are
building a lexicon for your machine translation system or question
answering system, and you need to decide on the parts of speech for
some words.  You look in a book and you find some tests for
distinguishing determiners and adjectives.  You have to apply the
tests, imperfect as they are, and make your decisions.  
\\[6pt]

\noindent
The exercise has several purposes:

\begin{enumerate}
\item You will learn to apply tests.
\item You will learn to interpret the results of tests.
\item You will encounter problems in categorizing words into parts of
speech.  
\end{enumerate}

\subsection{The Tests: distributional and morphological properties of
predeterminers, determiners, and adjectives in English}

\subsubsection{Determiner Test 1:}  

{\bf Test:} Determiners do not co-occur with {\it
the\/} and {\it a\/}.\\[6pt]

\noindent
{\bf Example:}  Is the word {\it this\/} a determiner? \\[6pt]

\noindent
{\bf Test Sentences:}
\examples{
\item \bad{*} The this book is about linguistics.
\item \bad{*} This the book is about linguistics.
\item \bad{*} A this book is about linguistics.
\item \bad{*} This a book is about linguistics.}

\noindent
{\bf Conclusion:} The word {\it this\/} passes Test 1 for determiners.

\subsubsection{Determiner Test 2:} 

{\bf Test:} If a determiner can occur with singular count nouns, it makes them acceptable.\\[6pt]

\noindent
You probably need to know some background in order to understand this
test.  English has count nouns and mass nouns, as do many other
languages.  Count nouns can occur with cardinal numbers or with {\it
a\/}.  Mass nouns can occur with {\it some\/}.  

\noindent
{\bf Count nouns:}
\examples{
\item Two books are on the table.
\item A book is on the table.
\item Twenty students are in the class.
\item A student is in the lounge.}

\noindent
{\bf Mass nouns:}
\examples{
\item Some sand is on the table.
\item \bad{*} A sand is on the table. 
\item \bad{*} Two sands are on the table.
\item Some information is available on the Web.
\item \bad{*} An information is available on the Web.
\item \bad{*} Two informations are available on the Web.
}

\noindent
The next fact is critical for Test 2:  Singular count nouns cannot
occur without a determiner in English:

\examples{
\item \bad{*} Book is on the table.
\item \bad{*} I saw book.
\item \bad{*} Student studied. 
\item \bad{*} I talked to student.}

\noindent
Singular count nouns are fine with a determiner:

\examples{
\item The/a book is on the table.
\item I saw the/a book.
\item The/a student studied.
\item I talked to the/a student.}

\noindent 
{\bf Example:} Is the word {\it this\/} a determiner?\\[6pt]

\noindent
{\bf Test Sentences:}
\examples{
\item This book is on the table.
\item I saw this book.
\item This student studied.
\item I talked to this student.}

\noindent
{\bf Conclusion:} {\it This\/} passes Test 2 for determiners.\\[6pt]

\noindent
{\bf Example:} Is the word {\it these\/} a determiner?\\[6pt]

\noindent
{\bf Conclusion:}  Test 2 for determiners is not applicable to {\it
these\/} because {\it these\/} only occurs with plural nouns.  

\subsubsection{Determiner Test 3:}  

\noindent
{\bf Test:} Determiners that are about
quantities can participate in a {\it partitive\/} construction.\\[6pt]

\noindent
In Examples \ex{0}a and b, the partitive construction is {\it each of
the students\/}.  It is called partitive because it is talking about
part of the set of students.  

\examples{
\item Each of the students has studied.
\item I talked to each of the students.}

\noindent
This test is not applicable to {\it a\/}, {\it the\/}, {\it this\/},
{\it that\/}, {\it these\/}, and {\it those\/} because they are not
about quantities.  They express definiteness and proximity.  

\subsubsection{Predeterminer Test:}

\noindent
{\bf Test:} There is just one test for predeterminers.  They can occur
before {\it a\/} or {\it the\/}.  

\examples{
\item {\it What\/} a party it was!
\item I never saw {\it so big\/} an elephant.
\item {\it All\/} the students left.}

\subsubsection{Adjective Test 1:} 

\noindent
{\bf Test:} Most adjectives can occur between {\it the\/} or {\it a\/} and a noun.

\examples{
\item The {\it blue\/} book is on the table.
\item A {\it blue\/} book is on the table. 
\item I saw a {\it blue\/} book.
\item I saw the {\it blue\/} book.}

\subsubsection{Adjective Test 2:} 

\noindent {\bf Test:} Most adjectives can occur in predicative
position, after verbs like {\it be\/}, {\it become\/}, {\it seem\/},
or {\it look\/}.

\examples{
\item The test seemed {\it difficult\/}.
\item The book was {\it blue\/}.
\item The cut became {\it infected\/}.
\item The cake looked {\it yummy\/}.}

\noindent
Some adjectives can only occur in predicative position:

\examples{
\item \bad{*} I saw an asleep child.
\item The child was asleep. 
\item \bad{*} The ahead runner won the race.
\item The runner was ahead.}

\subsubsection{Adjective Test 3:}  

\noindent {\bf Test:} Adjectives that describe gradable properties
have comparative and superlative forms:

\examples{
\item This copy is {\it darker\/}.
\item The {\it darker\/} copy is better. 
\item The {\it darkest\/} copy is not good.
\item This student is {\it more studious\/}.
\item The {\it most studious\/} student won a prize.}

\subsubsection{Adjective Test 4:} 

\noindent
{\bf Test:} Adjectives that describe gradable
properties can be modified with {\it very\/}.

\examples{
\item That book is very blue.
\item The very light print is not readable.}

\subsubsection{Adjective Test 5:}  

\noindent
{\bf Test:}
Adjectives that describe gradable
properties can be modified by {\it so\/} in predicative positions, but
not pre-nominal positions:

\examples{
\item That book is so blue.
\item The sky seemed so dark.}

\examples{
\item \bad{*} I saw the so blue book.
\item \bad{*} I saw so blue water. 
\item \bad{*} The so light print is not readable.}

\noindent
Don't get confused by this:  an adjective with {\it so\/} cannot occur
between a determiner and a noun, but it can occur as a predeterminer,
before the determiner:

\example{I never saw so big an elephant.}

\subsubsection{Determiner Test 4:} 

\noindent
{\bf Test:}
A determiner that describes a gradable property may be modified with
{\it so\/}.  {\bf In order to pass this test, the word must be
in pre-nominal position.}

\example{He made so many mistakes.}

\noindent
{\bf  Determiner Test~4 and Adjective Test~5 are easily
confusable, and in fact, some pieces of data might be relevant to both
tests.  In order to pass Adjective Test~5, the word must be able to
appear with {\it so\/} in predicative position, but not in prenominal
position.  In order to pass Determiner Test~4, the word must be
gradable and occur with {\it so\/} in prenominal position.}

\subsubsection{Adjective Test 6:} 

\noindent
{\bf Test:}
Another partitive construction:
Gradable adjectives may occur in this construction.

\examples{
\item The {\it largest\/} of the books couldn't fit in the box.
\item I have addressed the {\it most important\/} of your criticisms.}

\noindent
{\bf Determiner Test~3 and Adjective Test~6 are easily confused.
Determiner Test~3 is about partitive constructions like {\it many of
the students\/}.  Adjective Test~6 is about a construction that
involves a superlative plus a partitive ({\it the largest of the
boxes\/}).}

\subsection{Applying the tests and interpreting the results}

Write two things in each cell of the following table: (1) P if the
word passed the test or F if the word failed and (2) the number of the
example that supports your conclusion.  Leave the cell blank if there
was no relevant data.  Use my grammaticality judgments.  \\[10pt]

\noindent
{\bf There are a few possibilities:

\begin{itemize}
\item There was no relevant data:  leave the cell blank.
\item There is one piece of relevant data: put the example number and
the test result (P or F) in the cell.
\item There is more than one piece of relevant data, and both have the
same result.  We will count it right if you list one example number in
the cell.
\item There is more than one piece of relevant data, and the results
are different.  This might or might not arise depending on how you
interpret the tests.  If you think you have found a case like this,
write both results and both example numbers in the cell.
\end{itemize}}

\begin{tabular}{|l|l|l|l|l|}
\hline
 & {\bf enough} & {\bf sufficient} & {\bf much} & {\bf many}\\
\hline
\hline
{\bf PreDet} & & & &\\
\hline
\hline
{\bf Det1} & & & &\\
\hline
{\bf Det3} & & & &\\
\hline
{\bf Det4} & & & &\\
\hline
\hline
{\bf Adj1} & & & &\\
\hline
{\bf Adj3} & & & &\\
\hline
{\bf Adj4} & & & &\\
\hline
{\bf Adj5} & & & &\\
\hline
{\bf Adj6} & & & &\\
\hline
\end{tabular}

\examples{
\item \bad{*} Enough the books were given to the class.
\item \bad{*} The schoolboard provided the enough books.
\item The student has read enough of the books.
\item \bad{*} The bank gave them so enough money.
\item \bad{*} The funds were so enough.
\item \bad{*} The funds were very enough.
\item \bad{*} The most enough of the funds.}

\examples{
\item The accounts were filled with the sufficient funds.
\item The banker gave them a sufficient amount.
\item \bad{*} Sufficient of the books were given to the class.
\item These funds were very/so/more sufficient.
\item The most sufficient of the funds.}

\examples{
\item \bad{*}Much the/a water was spilled.
\item \bad{*}The much water was spilled.
\item Much of the water was spilled.
\item So much water was spilled.
\item The water was so much.}

\examples{
\item Many a student has taken this class.
\item I remember the many students who have taken this class.
\item Many of the students have taken this class.
\item I saw very many students. 
\item So many students have taken this class.
\item The problems were so many.}

%% Huddleston and Pullum: ``Many'' is a determiner with one unusual
%% property; it can be modified for grade as in ``very many''.  The
%% predeterminer thing (many a) is a fixed expression, so it doesn't count.

\noindent
{\bf Extra Credit:} One half point for each comment or question about
this exercise.\\[8pt]

\noindent
{\bf Actually, you will only get extra credit if your comments
or questions show an understanding of the material.  It's ok to
disagree, because there certainly is a lot to question and criticize.  

Some ideas for extra credit:  

\begin{itemize}
\item What do you think of the claim that parts of speech can be
identified by their distribution and morphological properties?  Does
it satisfy the scientific criteria of falsifiability and
reproducibility?  Maybe the claim is basically right, but it's really
hard to get the tests right.  Or maybe you have another idea for a better
theory of parts of speech, maybe something statistical or probablistic?

\item Re-formulate or disqualify some of the tests.  

\item Supply additional relevant data. You might want to consider
these.  (Add your own grammaticality judgments.) {\it the so
sufficient funds, I gave them so sufficient funds, most enough funds,
most sufficent funds, very much water, very many students\/}

\item Draw a conclusion about whether each word is a predeterminer,
determiner, or adjective, or whether it falls into more than one of these
categories, or whether if falls into none of these categories.  
\end{itemize}}

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

\noindent
Assume the following phrase structure rules:

\begin{verbatim}
S --> NP  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}

\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 I like 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 I like 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.

\end{document}
