diff --git a/text/paper_01/pre-paper.pdf b/text/paper_01/pre-paper.pdf
index 9ec5929..9767a67 100644
Binary files a/text/paper_01/pre-paper.pdf and b/text/paper_01/pre-paper.pdf differ
diff --git a/text/paper_01/pre-paper.tex b/text/paper_01/pre-paper.tex
index ded2826..11e9b74 100644
--- a/text/paper_01/pre-paper.tex
+++ b/text/paper_01/pre-paper.tex
@@ -74,6 +74,7 @@ citecolor=blue,
 \newcommand{\probfact}[2]{\ensuremath{#1\!::\!#2}}
 \newcommand{\tcgen}[1]{\ensuremath{\widehat{#1}}}
 \newcommand{\lfrac}[2]{\ensuremath{{#1}/{#2}}}
+\newcommand{\condsymb}[2]{\ensuremath{p{#1}\_{#2}}}
 
 \newcommand{\todo}[1]{{\color{red!50!black}(\emph{#1})}}
 \newcommand{\remark}[2]{\uwave{#1}~{\color{green!40!black}(\emph{#2})}}
@@ -781,7 +782,15 @@ We continue with the specification from Equation \eqref{eq:example.1}.
 %
 \subsection{An example involving Bayesian networks}
 
-As it turns out, our framework is suitable to deal with more sophisticated cases, for example cases involving Bayesian networks. In order to illustrate this, in this section we see how the classical example of the Burglary, Earthquake, Alarm \cite{Judea88} works in our setting. This example is a commonly used example in Bayesian networks because it illustrates reasoning under uncertainty.  The gist of example is given in \cref{Figure_Alarm}. It involves a simple network of events and conditional probabilities. 
+\franc{Cometários:}
+\begin{itemize}
+    \item Há uma macro, $\backslash\text{pr}\{A\}$, para denotar a função de probabilidade, $\pr{A}$ em vez de $P(A)$. Já agora, para a condicional também há um comando, $\backslash\text{given}$: $\pr{A \given B}$.
+    \item E, claro, para factos+probabilidades: $\probfact{p}{a}$.
+    \item A designação dos `pesos' não está consistente: $pj\_a$ e $a\_be$. Fiz uma macro (hehe) para sistematizar isto: \condsymb{a}{bnc}
+\end{itemize}
+
+
+As it turns out, our framework is suitable to deal with more sophisticated cases, \replace{for example}{in particular} cases involving Bayesian networks. In order to illustrate this, in this section we see how the classical example of the Burglary, Earthquake, Alarm \cite{Judea88} works in our setting. This example is a commonly used example in Bayesian networks because it illustrates reasoning under uncertainty.  The gist of example is given in \cref{Figure_Alarm}. It involves a simple network of events and conditional probabilities. 
 
 The events are: Burglary ($B$), Earthquake ($E$), Alarm ($A$), Mary calls ($M$) and John calls ($J$). The initial events $B$ and $E$ are assumed to be independent events that occur with probabilities $P(B)$ and $P(E)$, respectively. There is an alarm system that can be triggered by either of the initial events $B$ and $E$. The probability of the alarm going off is a conditional probability given that $B$ and $E$ have occurred. One denotes these probabilities, as per usual,  by $P(A|B)$, and $P(A|E)$. There are two neighbours, Mary and John who have agreed to call if they hear the alarm. The probability that they do actually call is also a conditional probability denoted by $P(M|A)$ and $P(J|A)$, respectively.
 
@@ -856,7 +865,7 @@ The events are: Burglary ($B$), Earthquake ($E$), Alarm ($A$), Mary calls ($M$) 
 \end{figure}
 
 
-Considering the probabilities given in \cref{Figure_Alarm} we obtain the following specification
+Considering the probabilities given in \cref{Figure_Alarm} we obtain the following spe\-ci\-fi\-ca\-tion
 
 \begin{equation*}
     \begin{aligned}
@@ -871,8 +880,8 @@ For the table giving the probability $P(M|A)$ we obtain the specification:
 
 \begin{equation*}
     \begin{aligned}
-        &\probfact{0.9}{pm\_a},\cr
-        &\probfact{0.05}{pm\_na},\cr
+        \probfact{0.9}{pm\_a}&,\cr
+        \probfact{0.05}{pm\_na}&,\cr
          m & \leftarrow a, pm\_a,\cr
          \neg m & \leftarrow a, \neg pm\_a.
             \end{aligned}
--
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