Made the definition of Event more readable.

2022Migration/articleMigrationFACS.tex

@@ -522,20 +522,26 @@ \subsection{Information Systems}
    Events are categorized by what part of the data set changes.
 
 \begin{definition}[Event]
-   Let $R \subseteq \Rels$ and $I \subseteq \Rels$ be sets of relations, and let $\infsys=\pair{\schema}{\dataset}$ and  $\infsys'=\pair{\schema}{\dataset'}$ be information systems, and:
-      \begin{align}
-      \triples_{\dataset} - (\Triple{\Atoms}{(R \cup I)}{\Atoms}) &= \triples_{\dataset'} - (\Triple{\Atoms}{(R \cup I)}{\Atoms})
+   Let $R \subseteq \Rels$ and $I \subseteq \Rels$ be sets of relations,
+   and let $\infsys=\pair{\schema}{\dataset}$ and  $\infsys'=\pair{\schema}{\dataset'}$ be information systems,
+   then $\infsys\xrightarrow[I]{R} \infsys'$ is an event if and only if:
+   \begin{align}
+      \triple{a}{r}{b}\in\triples_{\dataset}-\triples_{\dataset'}&\Rightarrow\ r\in R
    \label{eqn:eventUnchanged}\\
-      \triples_{\dataset} - (\Triple{\Atoms}{R}{\Atoms}) &\subseteq \triples_{\dataset'} - (\Triple{\Atoms}{R}{\Atoms})
+      \triple{a}{r}{b}\in\triples_{\dataset'}-\triples_{\dataset}&\Rightarrow\ r\in(R \cup I)
    \label{eqn:eventInsert}
    \end{align}
-%   Then we say that $\pair{\pair{\schema}{\dataset}}{\infsys'}$ is an event with scope $R$ inserting in $I$.
-   Then we say that $\infsys\xrightarrow[I]{R} \infsys'$ is an event
-   that brings the system $\infsys$ to $\infsys'$ inserting pairs in relations from $I$ and updating (i.e. deleting and inserting) pairs in $R$.
-%   We use the notation $\pair{\schema}{\dataset} \xrightarrow[I]{R} \infsys'$ to indicate this.
+   % was:
+   % \begin{align}
+   %    \triples_{\dataset} - (\Triple{\Atoms}{(R \cup I)}{\Atoms}) &= \triples_{\dataset'} - (\Triple{\Atoms}{(R \cup I)}{\Atoms})
+   % \label{eqn:eventUnchanged}\\
+   %    \triples_{\dataset} - (\Triple{\Atoms}{R}{\Atoms}) &\subseteq \triples_{\dataset'} - (\Triple{\Atoms}{R}{\Atoms})
+   % \label{eqn:eventInsert}
+   % \end{align}
+   We say that event $\infsys\xrightarrow[I]{R} \infsys'$ brings the system $\infsys$ to $\infsys'$ inserting pairs in relations from $I$ and deleting pairs in relations from $R$.
 \end{definition}
 
-   equation~\ref{eqn:eventUnchanged} states that the triples of those for relations in $I$ or $R$ are the only ones to have changed, and equation~\ref{eqn:eventInsert} states that of the ones that are only in $I$, no triples were removed.
+   Equation~\ref{eqn:eventUnchanged} states that the triples of those for relations in $I$ or $R$ are the only ones to have changed, and equation~\ref{eqn:eventInsert} states that of the ones that are only in $I$, no triples were removed.
    %If $I$ or $R$ is the empty set, we omit it from the arrow, so $\infsys \xrightarrow{R} \infsys'$ is a notation for $\infsys \xrightarrow[\emptyset]{R} \infsys'$.
 
 \begin{definition}[Inserting event]