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\title{}
\author{}

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\begin{document}
\maketitle


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For each sentence we require that if the sentence is about frame elements then there is no not annotated word equal to a frame element name in the database (i.e. all frame element names are properly annotated).

\[
\begin{array}{@{\hspace{5pt}}l}
\forall 
\hspace*{5pt}
\mbox{\em doc}
^{
\mathsf{Keep}
}
\hspace*{5pt}
{\scriptscriptstyle \in}
\hspace*{5pt}
\mathtt{getFNDocs}
\left(
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mathtt{fnDocu}
,
\\
\mathtt{repHead}
\left(
\mathtt{fnDocu}
\right)
,
\\
\mathsf{trfn3.tex}
\\
\end{array}
\right)
\hspace*{5pt}
\bullet 
\\
\begin{array}{@{\hspace{5pt}}l}
\forall 
\hspace*{5pt}
\mbox{\em sentence}
^{
\mathsf{Keep}
}
\hspace*{5pt}
{\scriptscriptstyle \in}
\hspace*{5pt}
\mathtt{getSentences}
\left(
\mbox{\em doc}
\right)
\hspace*{5pt}
\bullet 
\\
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mathtt{isAboutFE}
\left(
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mathtt{map}
\left(
\mathtt{content}
,
\mbox{\em sentence}
\right)
\\
\end{array}
\right)
\\
\\
\end{array}
\\
\implies 
\\
\left(
\begin{array}{@{\hspace{5pt}}l}
\forall 
\hspace*{5pt}
\mbox{\em context}
^{
\mathsf{Keep}
}
\hspace*{5pt}
{\scriptscriptstyle \in}
\hspace*{5pt}
\mbox{\em sentence}
\hspace*{5pt}
\bullet 
\\
\begin{array}{@{\hspace{5pt}}l}
\forall 
\hspace*{5pt}
\mbox{\em word}
^{
\mathsf{Keep}
}
\hspace*{5pt}
{\scriptscriptstyle \in}
\hspace*{5pt}
\mathtt{map}
\left(
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mathtt{trimS}
,
\\
\mathtt{wordsS}
\left(
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mathtt{getText}
\left(
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mathtt{content}
\left(
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mbox{\em context}
\\
\end{array}
\right)
\\
\end{array}
\right)
\\
\end{array}
\right)
\\
\end{array}
\right)
\hspace*{5pt}
\bullet 
\\
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mathtt{mightBeFEName}
\left(
\mbox{\em word}
\right)
\\
\implies 
\\
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mathtt{null}
\left(
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mathtt{getFEByName}
\left(
\mathtt{fnDB}
,
\mbox{\em word}
\right)
\\
\end{array}
\right)
\\
\\
\end{array}
\\
\end{array}
\\
\end{array}
\\
\end{array}
\right)
\\
\end{array}
\\
\end{array}
\\
\end{array}
\]
\end{document}
