@InProceedings{narisawa13,
  author    = {Narisawa, Katsuma  and  Watanabe, Yotaro  and  Mizuno, Junta  and  Okazaki, Naoaki  and  Inui, Kentaro},
  title     = {Is a 204 cm Man Tall or Small ? Acquisition of Numerical Common Sense from the Web},
  booktitle = {Proc. 51st ACL (Long papers)},
  month     = {August},
  year      = {2013},
  pages     = {382--391},
  url       = {http://www.aclweb.org/anthology/P13-1038}
  annote = {This paper presents novel methods for modeling numerical common
sense: the ability to infer whether a given number (e.g., three billion) is
large, small, or normal for a given context (e.g., number of people facing a
water shortage). We first discuss the necessity of numerical common sense in
solving textual entailment problems. We explore two approaches for acquiring
numerical common sense. Both approaches start with extracting numerical
expressions and their context from the Web. One approach estimates the
distribution of numbers co-occurring within a context and examines whether a
given value is large, small, or normal, based on the distribution.  Another
approach utilizes textual patterns with which speakers explicitly expresses
their judgment about the value of a numerical expression. Experimental
results demonstrate the effectiveness of both approaches.\\
\\
An example of issues tacked by this paper is
\begin{verbatim}
t : Before long, 3b people will face a water shortage in the world.
h : Before long, a serious water shortage will occur in the world.
\end{verbatim}

t entails h - but recognizing this is frustratingly difficult. The paper assumes this inference is decomposable into three phases:
\begin{verbatim}
3b people face a water shortage.
   <==> [3,000,000,000 people] face a water shortage.
   |= [many people] face a water shortage.
   |= a serious water shortage.
\end{verbatim}

This paper collected numerical expressions from a large corpus of web pages and hand-categorized them into nine broad categories. Most papers fall into category 1, "Numerical Matching" which deals with aligning numerical expressions. For example:
t: It is said that there are about 2.2 million alcoholics in the whole country.
h: It is estimated that there are over 800 thousand people who are alcoholics.

The procedure used had three broad steps:
\begin{enumerate}
\item Find numbers in the text
\item Check terms that precede or follow the number to transform into equivalent units using a dictionary
\item Look for modifiers like 'roughly', or 'above' and mark the corresponding flags.
\end{enumerate}

Context or common sense is found using a search of the context of the sentence, with most importance being given to the following categories (if present): verb, subject noun, object noun, prepositions. An alternative approach looked for textual clues like 'as much as', 'as large as', 'as small as' in sentences with similar numerical expressions.

The results seem to be satisfactory. An F1-Score of 0.851, 0.790, and 0.464 was achieved with the second approach and 0.695, 0.844, and 0.262 with the first approach (for large, normal and small tags respectively).
}
}