deletions | additions       diff --git a/Even_after_all_the.tex b/Even_after_all_the.tex  index b56ebc6..007e37e 100644  --- a/Even_after_all_the.tex  +++ b/Even_after_all_the.tex 
...
Even after all the aforementioned facts about Marko and Alberto's ``knowing" relationship are encoded in $T_x$, still more information is required to fully understand what is meant by Marko ``knowing" Alberto. What is the nature of the scholarly data set that they analyzed? Who did what for the analysis? Did they ever socialize outside of work when Alberto was visiting LANL? What was the conversation that they had with Leo Egghe like? Can their \texttt{foaf:knows} relationship ever be fully understood? Only an infinite recursion into their histories, experiences, and subjective worlds could reveal the ``true" meaning of (\texttt{lanl:marko}, \texttt{foaf:knows}, \texttt{ucla:apepe}). Only when $T_\tau = R$, (Note: For the purpose of this part of the argument, $R$ is assumed to be a theoretical graph instance that includes all statements about the world) that is, when their relationship is placed within the broader context of the world as a whole, does the complete picture emerge. However, with respect to those triples that provide the most context, a $|T_\tau| \ll |R|$ suffices to expose the more essential aspects of (\texttt{lanl:marko}, \texttt{foaf:knows}, \texttt{ucla:apepe}). (Note: A fuzzy set is perhaps the best representation of a dilated triple \cite{zadeh:fuzzy1965}. In such cases, a membership function $\mu_{T_\tau}: R \rar [0,1]$ would define the degree to which every triple in $R$ is in $T_\tau$. However, for the sake of simplicity and to present the proposed model within the constructs of the popular named graph formalism, $T_\tau$ is considered a classical set. Moreover, a fuzzy logic representation requires an associated membership valued in $[0,1]$ which then requires further statement reification in order to add such metadata. With classic bivalent logic, $\{0,1\}$ iss captured by the membership or non-membership of the statement in $T_\tau$.) (Note: The choices made in the creation of a dilated triple are determined at the knowledge-level \cite{know:newell1982}. The presentation here does not suppose the means of creation, only the underlying representation and utilization of such a representation.)