\batchmode
\documentstyle[twoside,11pt,psfig]{article}
\makeatletter %
\input epsf

\title{An Empirical Approach to Temporal Reference Resolution}

\author{
{Janyce M. Wiebe}, {Thomas P. O'Hara}, \\
{Thorsten~\"{O}hrstr\"{o}m-Sandgren}, and {Kenneth J. McKeever} \\
\\
\email{wiebe@cs.nmsu.edu}, \email{tomohara@cs.nmsu.edu}, \\
\email{sandgren@lucent.com}, \email{kmckeeve@redwood.dn.hac.com} \\
\\
{
Department of Computer Science and \\
Computing Research Laboratory \\
New Mexico State University \\
Las Cruces, NM 88003}}
\par



\makeatletter
\count@=\the\catcode`\_ \catcode`\_=8 
\newenvironment{tex2html_wrap}{}{} \catcode`\_=\count@
\makeatother
\let\mathon=$
\let\mathoff=$
\ifx\AtBeginDocument\undefined \newcommand{\AtBeginDocument}[1]{}\fi
\newbox\sizebox
\setlength{\hoffset}{0pt}\setlength{\voffset}{0pt}
\addtolength{\textheight}{\footskip}\setlength{\footskip}{0pt}
\addtolength{\textheight}{\topmargin}\setlength{\topmargin}{0pt}
\addtolength{\textheight}{\headheight}\setlength{\headheight}{0pt}
\addtolength{\textheight}{\headsep}\setlength{\headsep}{0pt}
\setlength{\textwidth}{349pt}
\newwrite\lthtmlwrite
\makeatletter
\let\realnormalsize=\normalsize
\global\topskip=2sp
\def\preveqno{}\let\real@float=\@float \let\realend@float=\end@float
\def\@float{\let\@savefreelist\@freelist\real@float}
\def\end@float{\realend@float\global\let\@freelist\@savefreelist}
\let\real@dbflt=\@dbflt \let\end@dblfloat=\end@float
\let\@largefloatcheck=\relax
\def\@dbflt{\let\@savefreelist\@freelist\real@dbflt}
\def\adjustnormalsize{\def\normalsize{\mathsurround=0pt \realnormalsize
 \parindent=0pt\abovedisplayskip=0pt\belowdisplayskip=0pt}\normalsize}%
\def\lthtmltypeout#1{{\let\protect\string\immediate\write\lthtmlwrite{#1}}}%
\newcommand\lthtmlhboxmathA{\adjustnormalsize\setbox\sizebox=\hbox\bgroup}%
\newcommand\lthtmlvboxmathA{\adjustnormalsize\setbox\sizebox=\vbox\bgroup%
 \let\ifinner=\iffalse }%
\newcommand\lthtmlboxmathZ{\@next\next\@currlist{}{\def\next{\voidb@x}}%
 \expandafter\box\next\egroup}%
\newcommand\lthtmlmathtype[1]{\def\lthtmlmathenv{#1}}%
\newcommand\lthtmllogmath{\lthtmltypeout{l2hSize %
:\lthtmlmathenv:\the\ht\sizebox::\the\dp\sizebox::\the\wd\sizebox.\preveqno}}%
\newcommand\lthtmlfigureA[1]{\let\@savefreelist\@freelist
       \lthtmlmathtype{#1}\lthtmlvboxmathA}%
\newcommand\lthtmlfigureZ{\lthtmlboxmathZ\lthtmllogmath\copy\sizebox
       \global\let\@freelist\@savefreelist}%
\newcommand\lthtmldisplayA[1]{\lthtmlmathtype{#1}\lthtmlvboxmathA}%
\newcommand\lthtmldisplayB[1]{\edef\preveqno{(\theequation)}%
  \lthtmldisplayA{#1}\let\@eqnnum\relax}%
\newcommand\lthtmldisplayZ{\lthtmlboxmathZ\lthtmllogmath\lthtmlsetmath}%
\newcommand\lthtmlinlinemathA[1]{\lthtmlmathtype{#1}\lthtmlhboxmathA  \vrule height1.5ex width0pt }%
\newcommand\lthtmlinlineA[1]{\lthtmlmathtype{#1}\lthtmlhboxmathA}%
\newcommand\lthtmlinlineZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
  \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetinline}
\newcommand\lthtmlinlinemathZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
  \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetmath}
\def\lthtmlsetinline{\hbox{\vrule width.1em\vtop{\vbox{%
  \kern.1em\copy\sizebox}\ifdim\dp\sizebox>0pt\kern.1em\else\kern.3pt\fi
  \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
\def\lthtmlsetmath{\hbox{\vrule width.1em\vtop{\vbox{%
  \kern.1em\kern0.8 pt\hbox{\hglue.17em\copy\sizebox\hglue0.8 pt}}\kern.3pt%
  \ifdim\dp\sizebox>0pt\kern.1em\fi \kern0.8 pt%
  \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
\def\centerinlinemath{%\dimen1=\ht\sizebox
  \dimen1=\ifdim\ht\sizebox<\dp\sizebox \dp\sizebox\else\ht\sizebox\fi
  \advance\dimen1by.5pt \vrule width0pt height\dimen1 depth\dimen1 
 \dp\sizebox=\dimen1\ht\sizebox=\dimen1\relax}

\def\lthtmlcheckvsize{\ifdim\ht\sizebox<\vsize\expandafter\vfill
  \else\expandafter\vss\fi}%
\makeatletter \tracingstats = 1 


\begin{document}
\pagestyle{empty}\thispagestyle{empty}%
\lthtmltypeout{latex2htmlLength hsize=\the\hsize}%
\lthtmltypeout{latex2htmlLength vsize=\the\vsize}%
\lthtmltypeout{latex2htmlLength hoffset=\the\hoffset}%
\lthtmltypeout{latex2htmlLength voffset=\the\voffset}%
\lthtmltypeout{latex2htmlLength topmargin=\the\topmargin}%
\lthtmltypeout{latex2htmlLength topskip=\the\topskip}%
\lthtmltypeout{latex2htmlLength headheight=\the\headheight}%
\lthtmltypeout{latex2htmlLength headsep=\the\headsep}%
\lthtmltypeout{latex2htmlLength parskip=\the\parskip}%
\lthtmltypeout{latex2htmlLength oddsidemargin=\the\oddsidemargin}%
\makeatletter
\if@twoside\lthtmltypeout{latex2htmlLength evensidemargin=\the\evensidemargin}%
\else\lthtmltypeout{latex2htmlLength evensidemargin=\the\oddsidemargin}\fi%
\makeatother
\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
\lthtmlfigureA{figure45}%
\begin{figure}\begin{center}
\begin{tabular}{|lll|}
\hline
\multicolumn{3}{|c|}{{\it Temporal context:
Tuesday 28 September}} \\
\hline
s1& 1&   On Thursday I can only meet after two pm \\
   &2&  From two to four \\
   &3&     Or two thirty to four thirty \\
   &4&    Or three to five \\
s2& 5&   Then how does from two thirty to four thirty seem to you \\
   &6&   On Thursday \\
s1& 7&  Thursday the thirtieth of September \\
\hline
\end{tabular}
\end{center}
\end{figure}%
\lthtmlfigureZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figurestar60}%
\begin{figure*}\begin{center}
\vspace*{2mm}
\begin{tabular}{|lllll|}
\hline
((start-month, & start-date, & start-day-of-week, & start-hour\&minute,
& start-time-of-day) \\
\hspace*{1mm}(end-month, & end-date, & end-day-of-week, & end-hour\&minute, &
end-time-of-day))  \\
\hline
\end{tabular}
\end{center}
\end{figure*}%
\lthtmlfigureZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1219}%
$\kappa$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1211}%
\begin{displaymath}\kappa = \frac{Pa - Pe}{1 - Pe} \end{displaymath}%
\lthtmldisplayZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1237}%
$\sum_{j=1}^{M}{n_{ij}} = K$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1239}%
$C_j = \sum_{i=1}^{N} n_{ij}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1243}%
$p_j = \frac{C_j}{N \times K}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1247}%
$N \times K$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline92}%
$\mbox{$\bullet$}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1212}%
\begin{displaymath}Pe = \sum_{j=1}^{M} p^{2}_{j} \end{displaymath}%
\lthtmldisplayZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1213}%
\begin{displaymath}S_i = \frac{\sum_{j=1}^{M} \left( \begin{array}{c} n_{ij} \\2  
\end{array} \right)}
{\left( \begin{array}{c} K \\2  \end{array} \right)} \end{displaymath}%
\lthtmldisplayZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1214}%
\begin{displaymath}Pa = \frac{1}{N} \sum_{i=1}^{N} S_i \end{displaymath}%
\lthtmldisplayZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1267}%
$\kappa_{avg}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlfigureA{figurestar146}%
\begin{figure*}\begin{center}

\noindent
{\em
\begin{tabular}{|lrclccc|}
\hline
      &     & day of week &      &             &    &               \\
      & $\nearrow$ &         & $\searrow$ &             &    &               \\
month &     &         &      & time of day & $\longrightarrow$ & hour\&minute  \\
      & $\searrow$ &         & $\nearrow$ &             &    &               \\
      &     & date    &      &             &    &               \\
\hline
\end{tabular}
}
\end{center}
\end{figure*}%
\lthtmlfigureZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsubsection}
\stepcounter{subsubsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1299}%
$\ldots$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
\stepcounter{subsubsection}
\stepcounter{subsubsection}
\stepcounter{subsubsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure296}%
\begin{figure}\begin{center}
\centerline{
\psfig{figure=f1id.eps,width=0.5\textwidth}}
\end{center}
\end{figure}%
\lthtmlfigureZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
\stepcounter{subsection}
\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure358}%
\begin{figure}\begin{center}
\centerline{
\psfig{figure=f2id.eps,width=0.99\textwidth}}
\end{center}
\end{figure}%
\lthtmlfigureZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1409}%
$\{ \}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1431}%
$\rightarrow$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure421}%
\begin{figure}\par\begin{center}
{\large\em Rules for deictic relations}
\end{center}
\par\begin{tabbing}
mm\=mm\=mm\=mm\=mm\=mm\=mm\=mm\= \kill
{\em\bf Rule D-simple:} All cases of the {\it simple}
deictic relation. \\
if there is a deictic term, $DT$ , in $TU$\space then \\
\>    return $\langle$0.9, merge($TU$ ,
resolve\_deictic($DT$ , {\bf$TodaysDate$ }))$\rangle$\space \\
 \\
{\em\bf Rule D-frame-of-reference:} The starting-time cases of the
{\it frame of reference} deictic relation. \\
if (most\_specific(starting\_fields($TU$ )) $<$\space {\bf time\_of\_day}) then \\
\> Let $f$\space be the most specific field in starting\_fields($TU$ ) \\
\> return 
$\langle$0.4, merge($TU$ , next($TU$$\rightarrow$$f$ , $TodaysDate$ ))$\rangle$\end{tabbing}
\begin{center}
{\large\em Rules for anaphoric relations}
\end{center}
\par\begin{tabbing}
mm\=mm\=mm\=mm\=mm\=mm\=mm\=mm\= \kill
{\em\bf Rule A-co-reference:} All cases of the {\it co-reference}
anaphoric relation. \\
for each non-empty Temporal Unit $TU_{fl}$\space from $FocusList$\space (starting with most recent) \\
\> if specificity($TU_{fl}$ ) $\leq$\space specificity($TU$ ) 
         and not empty merge($TU_{fl}$ , $TU$ ) then \\
\>  \> $CF$\space = 0.8 $-$\space distance\_factor($TU_{fl}$ , {\bf$FocusList$ }) \\
\>  \> return $\langle$$CF$ , merge($TU_{fl}$ , $TU$ )$\rangle$\space \\
 \\
\par {\em\bf Rule A-less-specific:} All cases of the {\it less-specific} anaphoric 
relation. \\
for each non-empty Temporal Unit $TU_{fl}$\space from $FocusList$\space (starting with most recent) \\
\> if specificity($TU_{fl}$ ) $>$\space specificity($TU$ ) 
      and not empty merge\_upper($TU_{fl}$ , $TU$ ) then \\
\> \> $CF$\space = 0.5 $-$\space distance\_factor($TU_{fl}$ , {\bf$FocusList$ }) \\
\> \> return $\langle$$CF$ , merge\_upper($TU_{fl}$ , $TU$ )$\rangle$\space \\
 \\
\par {\em\bf Rule A-frame-of-reference:} 
Starting-time case of the {\it frame of reference} anaphoric relation. \\
if (most\_specific(starting\_fields($TU$ )) $<$\space {\bf time\_of\_day}) then \\
\> for each non-empty Temporal Unit $TU_{fl}$\space from $FocusList$\space (starting with most recent) \\
\> \> if specificity($TU$ ) $\geq$\space specificity($TU_{fl}$ ) then \\
\> \> \> Let $f$\space be the most specific field in starting\_fields($TU$ ) \\
\> \> \> $CF$\space = 0.6 $-$\space distance\_factor($TU_{fl}$ , {\bf$FocusList$ }) \\
\> \> \> return 
$\langle$$CF$ , merge($TU$ , next($TU$$\rightarrow$$f$ , $TU_{fl}$$\rightarrow$ start\_date))$\rangle$\space \\
 \\
\par {\em\bf Rule A-modify:} All cases of the {\it modify} anaphoric relation. \\
if (specificity($TU$ ) $\geq$\space {\bf time\_of\_day}) then \\
\> for each non-empty Temporal Unit $TU_{fl}$\space from $FocusList$\space (starting with most recent) \\
\> \> if specificity($TU$ ) $\geq$\space specificity($TU_{fl}$ ) and
specificity($TU_{fl}$ ) $\geq$\space {\bf time\_of\_day} then \\
\> \> \> if not empty merge\_upper($TU_{fl}$ , $TU$ ) then \\
\> \> \> \> $CF$\space = 0.5 $-$\space distance\_factor($TU_{fl}$ , {\bf$FocusList$ }) \\
\> \> \> \> return $\langle$$CF$ , merge\_upper($TU_{fl}$ , $TU$ )$\rangle$\space \\
\end{tabbing}
\end{figure}%
\lthtmlfigureZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure597}%
\begin{figure}\begin{center}
\begin{tabular}{|l|c|c|}
\hline
 & \# TUs  & \# TUs specified anaphorically \\
\hline
CMU    & 196  & 167 \\%
\hline
NMSU   &  96  &  71 \\%
\hline
Total  & 292  & 238 \\
\hline
\end{tabular}
\end{center}
\end{figure}%
\lthtmlfigureZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure608}%
\begin{figure}\centerline{\psfig{figure=ana.ps,width=0.99\textwidth}}
\end{figure}%
\lthtmlfigureZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlfigureA{figure626}%
\begin{figure}\begin{center}
\centerline{
\psfig{figure=f3id.eps,width=0.15\textwidth}}
\end{center}
\end{figure}%
\lthtmlfigureZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure635}%
\begin{figure}\small
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
& \multicolumn{1}{c|}{1}  &  \multicolumn{1}{c|}{2} &  \multicolumn{1}{c|}{3}  & \multicolumn{1}{c|}{4}
& \multicolumn{1}{c|}{5}  & \multicolumn{1}{c|}{6}  \\
\hline
& Distance to & Subdialog? & Type of $TU_2$\space & $TU_2$\space  & $TU_2$\space a & Potential \\
& most recent &            &             & Correct?    & Competitor?                   & Cumulative  \\
   & appropriate & & & & & Errors \\
   & antecedent & & & & & \\
\hline
1 (07-37)   & 2      &  No        & Anaphoric,  &  Yes   &   Yes   &   21 \\
CMU         &        &            & main task   &        &         & \\
\hline
2 (07-63) &  2          &  No        & Habitual &       No & Yes            &   0 \\
CMU       &             &            &          &          &                & \\
\hline
3 (15-31)   & 2           &  No        & Anaphoric, &   Yes         &   Yes              & 4 \\
CMU      &             &            & main task      &  & & \\
\hline
4 (08-57)  & 2          &   Yes       & Reference    & No   &  Yes & 2 minor \\
NMSU     &            &             & outside dialog &   & & \\
\hline
5 (08-66)  &  3         &   Yes       & 1 deictic   &  Yes  & Yes  & 10   \\
NMSU      &            &             & 1 habitual  &  No   & Yes  &  (worst case) \\
\hline
6 (09-39)  &  2          & No          & habitual    & No   &  No   & 0 \\
NMSU       &             &            &          &          &                & \\
\hline
7 (09-09)&   3          & Yes         & 1 deictic   & Yes  & Yes  &  4 \\
NMSU     &             &             & 1 habitual  & No   &      & (worst
case) \\
\hline
8 (09-45)  &  3    & Borderline   & both habitual  & No & Yes   & 6 \\
NMSU      &        &              &                &    &      & \\
\hline 
9 (10-55) & 3 & Borderline & both habitual & No & Yes &
3 \\
NMSU     &             &             & &   &      &  \\
\hline
\par\end{tabular}
\end{center}
\end{figure}%
\lthtmlfigureZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure665}%
\begin{figure}\begin{center}
\begin{tabular}{|ll|}
\hline
\multicolumn{2}{|c|}{{\it Dialog Date:  Monday 10 May}}  \\
\hline
$TU_1$ :  & It's just that $\dots$\space this Thursday {\it [Thursday May 13]} is our second wedding
\\
         & anniversary and I don't know what to do.  \\
& $\langle$\space 31 non-temporal utterances about what to cook $\rangle $\space \\
& Did you go with my mother?  \\
$TU_2$ : &  With my mother? Yes.  I went at around six in the morning. \\
&  Did you and Maura go for a walk? \\
& No, no we didn't. \\
& Hmmmmm.   We got lazy. \\
& Ah Claudia. \\
$TU_3$\space & Well, yes.  Listen Lily.  What do you think if we see each
other on, \\
& on Thursday at six and I, at six? \\
\hline
\end{tabular}
\end{center}
\end{figure}%
\lthtmlfigureZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure684}%
\begin{figure}\begin{center}
\begin{tabular}{ll}
\multicolumn{2}{l}{{\it Correct Interpretation of the $TU_1$\space reference: Monday 22nd November}} \\
$TU_2$ : & of December?  \\
$TU_3$ : & of November.  \\
\end{tabular}
\end{center}
\end{figure}%
\lthtmlfigureZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure697}%
\begin{figure}\begin{center}
\centerline{
\psfig{figure=f5id.eps,width=0.5\textwidth}}
\end{center}
\end{figure}%
\lthtmlfigureZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure715}%
\begin{figure}\begin{center}
\begin{tabular}{|llll|}
\hline
\multicolumn{4}{|c|}{{\it Temporal context:
Tuesday 28 September}} \\
\hline
& s1& 1&   On Thursday I can only meet after two pm \\
&   &2&  From two to four \\
$TU_1$\space &   &3&     Or two thirty to four thirty \\
$TU_2$\space &   &4&    Or three to five \\
$TU_3$\space & s2& 5&   Then how does from two thirty to  \\
&  &  & four thirty seem to you \\
&   &6&   On Thursday \\
& s1& 7&  Thursday the thirtieth of September \\
\hline
\end{tabular}
\end{center}
\end{figure}%
\lthtmlfigureZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlfigureA{figure754}%
\begin{figure}\begin{center}
\centerline{
\psfig{figure=f4id.eps,width=0.2\textwidth}}
\end{center} 
\end{figure}%
\lthtmlfigureZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1809}%
$\mid$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1829}%
$p \le 0.05$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}

\end{document}
