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\title{Acquiring Word-Meaning Mappings \\for Natural Language Interfaces}

\author{Cynthia A. Thompson \\{\tt cindi@cs.utah.edu} \\
 School of Computing, University of Utah
  \\Salt Lake City, UT 84112-3320 \\~\\%
Raymond J. Mooney \\{\tt mooney@cs.utexas.edu} \\
Department of Computer Sciences,
University of Texas \\
Austin, TX 78712-1188}

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nn\=nn\=nn\=nn\=nn\=nn\=nn\= \kill
{\bf For} each phrase, $p$\space (of at most two words):\\
\> 1.1) Collect the training examples in which $p$\space appears\\
\> 1.2) Calculate LICS from (sampled) pairs of these examples' representations\\
\> 1.3) For each $l$\space in the LICS, add $(p, l)$\space to the set of candidate lexicon entries\\
{\bf Until} the input representations are covered, or no candidate
lexicon entries remain {\bf do}: \\
\> 2.1) Add the best (phrase, meaning) pair from the candidate entries to the lexicon \\
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{\bf Return} the lexicon of learned (phrase, meaning) pairs.
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\>Phrase \>\> LICS \> From Sentences \hspace{-4.2in}\rule[-0.03in]{4.5in}{.01in}\\
\> ``capital'': \>\> {\tt largest(\_,\_)} \> 1,4 \\
\>\>\> {\tt capital(\_,\_)} \> 1,7 \\
\>\>\> {\tt state(\_)} \> 1,7 \\
\> ``grande'': \>\> {\tt largest(\_,state(\_))} \>  1,2 \\
\>\>\> {\tt largest(\_,\_)} \> 1,4; 2,4 \\
\> ``estado'': \>\> {\tt largest(\_,state(\_))} \> 1,2 \\
\>\>\> {\tt state(\_)} \> 1,3; 1,7; 2,3; 2,6; 2,7; 3,6; 6,7 \\
\>\>\> {\tt (population(S,\_), state(S))} \> 1,6 \\
\>\>\> {\tt capital(\_,\_)} \> 1,7 \\
\>\>\> {\tt high\_point(\_,\_)} \> 2,7 \\
\>\>\> {\tt (state(S), loc(\_,S))} \> 3,7 \\
\> ``punta mas'': \>\> {\tt high\_point(\_,\_)} \> 2,7 \\
\>\>\> {\tt state(\_)} \> 2,7 \\
\> ``encuentra'': \>\> {\tt (state(S), loc(\_,S))} \> 3 \\
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nn ``capital'', {\tt population(S,\_),state(S)}): \= \kill
\underline{Candidate Lexicon Entry} \> \underline{Heuristic Value} \\
(``capital'', {\tt largest(\_,\_)}):\> $10(2^2/3) + 1(-1) = 12.33$\\
(``capital'', {\tt capital(\_,\_)}):\> 12.33\\%
(``capital'', {\tt state(\_,\_)}):\> 12.33\\%
(``grande'', {\tt largest(\_,state(\_))}):\> $10(2^2/3) + 1(-2) = 11.3$\\%
(``grande'', {\tt largest(\_,\_)}):\> $29$\\%
(``estado'', {\tt largest(\_,state(\_))}):\> $10(2^2/5) +1(-2) = 6$\\%
(``estado'', {\tt state(\_)}):\> $10(5^2/5) + 1(-1) = 49$\\%
(``estado'', {\tt (population(S,\_), state(S))}:\> 6\\%
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(``punta mas'', {\tt state(\_)}): \>
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$10(1^2/1) + 1(-2) =8$\space %
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{\bf Given:} A learned phrase-meaning pair $(l, g)$\\
\\
{\bf For} all sentence-representation pairs containing
$l$\space and $g$ , mark them as covered.\\
{\bf For} each  candidate phrase-meaning pair $(p, m)$ :\\
\> {\bf If} $p$\space occurs in some training pairs with $(l, g)$\space {\bf then} \\
\>\> {\bf If} the vertices of $m$\space intersect the vertices of $g$\space {\bf then}\\
\>\>\> {\bf If} all occurrences of $m$\space are now covered {\bf then} \\
\>\>\>\> Remove  $(p, m)$\space from the set of  candidate pairs. \\
\>\>\> {\bf Else} \\
\>\>\>\> Adjust the heuristic value of $(p,m)$\space as needed to account \\
\>\>\>\>\> for newly covered nodes of the training representations.\\
\>\>\> Generalize $m$\space to remove covered nodes, obtaining $m'$ , and \\
\>\>\> Calculate the heuristic value of the new candidate pair $(p,m')$ . \\
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\>\> calculate their heuristic values.
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nn\=nn\=nn\=nn\=nn\=nn\=nn\= \kill
Learn a lexicon with the examples annotated so far\\
1) {\bf For} each phrase in an unannotated sentence: \\
\> {\bf If} it has entries in the learned lexicon {\bf then} \\
\>\> its certainty is the average of the heuristic values of those entries\\
\> {\bf Else}, {\bf if} it is a one-word phrase {\bf then}\\
\>\> its certainty is zero \\
2) To rank sentences use: \\
\> \underline{Total certainty of phrases from step 1} \\
\>\> $\#$\space of phrases counted in step 1
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