Update 1-preliminaries.tex

blueprint/src/chapters/1-preliminaries.tex

@@ -2,17 +2,20 @@ \chapter{Preliminaries}
 % \label{chap:preliminaries}
 %\addcontentsline{toc}{chapter}{Preliminaries}
 
+This chapter provides the necessary prerequisites used throughout this project.
+We begin by introducing the notation that will be employed, followed by essential definitions and
+preliminary results required for formalising our arguments.
+
 \section{Notation}
-%\addcontentsline{toc}{section}{Notation}
 
-% \begin{center}
+% In this section, we define the notation and symbols that will be consistently used in this work.
+% Familiarity with these symbols is crucial for understanding the formal arguments and proofs presented later.
+
 \begin{tabular}{>{\centering}m{1.8cm} m{5.8cm}}
 \toprule
 \textbf{Symbol} & \multicolumn{1}{c}{\textbf{Description}} \\
 \midrule
 $\lnot$ & Logical negation \\
-$\top$  & Logical truth / Tautology \\
-$\bot$  & Logical falsity / Contradiction \\
 $\land$ & Logical conjunction \\
 $\lor$ & Logical inclusive disjunction \\
 $:=$   & Definition \\
@@ -38,7 +41,8 @@ \section{Notation}
 \newpage
 
 \section{Definitions}
-%\addcontentsline{toc}{section}{Definitions}
+
+In this section, each definition is articulated as clearly as possible to maximise clarity and precision.
 
 \begin{definition-pre}[Monoid]
     \label{def:monoid}