deletions | additions       diff --git a/the dilated triple model.tex b/the dilated triple model.tex  index 12e0e5d..3ee59b7 100644  --- a/the dilated triple model.tex  +++ b/the dilated triple model.tex 
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A single predicate URI does not provide the appropriate degrees of freedom required when modeling the nuances of an RDF relationship. The model proposed in this article enhances the expressiveness of a triple such that its meaning is considered within a larger context as defined by a graph structure. It thereby provides a machine with the ability to discern the more fine-grained context in which a statement relates its subject and object.  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}.\footnote{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. triple}.  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 $\tau \in T_\tau$.