deletions | additions       diff --git a/In_the_proposed_model.tex b/In_the_proposed_model.tex  index 3015fb2..9077bf2 100644  --- a/In_the_proposed_model.tex  +++ b/In_the_proposed_model.tex 
...
In the proposed model, every triple in an RDF graph is supplemented with other triples from the same RDF graph. The triple and its supplements form what is called a \textit{dilated triple}. Note: (Note:  The Oxford English dictionary provides two definitions for the word ``dilate": ``to expand" and ``to speak or write at length". It will become clear through the remainder of this article that both definitions suffice to succinctly summarize the presented model. model.)  \textbf{Definition 1. A Dilated Triple} Given a set of triples $R$ and a triple $\tau \in R$, a dilation of $\tau$ is a set of triples $T_\tau \subset R$ such that $\tau \in T_\tau$.  The dilated form of $\tau \in R$ is $T_\tau$. Informally, $T_\tau$ servers to elaborate the meaning of $\tau$. Formally, $T_\tau$ is a graph that at minimum contains only $\tau$ and at maximum contains all triples in $R$. The set of all non-$\tau$ triples in $T_\tau$ (i.e.~$T_\tau \setminus \tau$) are called \textit{supplementary triples} as they serve to contextualize, or supplement, the meaning of $\tau$. Finally, it is worth noting that every supplemental triple in $T_\tau$ has an associated dilated form, so that $T_\tau$ can be considered a set of nested sets. (The set of all dilated triples forms a \textit{dilated graph} denoted $\mca{T} = \bigcup_{\tau \in R} \{ T_\tau \}$.) An instance of $\tau$, its subject $s$, predicate $p$, object $o$, and its dilated form $T_\tau$, are diagrammed in Figure 1.