[DMDB] Intuition for FD and NF

semester4/dmdb/parts/00_relational-model_logic/00_model/01_keys.tex

@@ -1,12 +1,12 @@
 \subsubsection{Keys}
 \label{sec:relations-keys}
-\inlinedefinition[Candidate Key] The minimal set of fields that identify each tuple uniquely
+\inlinedefinition[Candidate Key] The minimal set of fields that identify each tuple uniquely (non-duplicate attributes (fields) typically)
 
 \inlinedefinition[Primary Key] A single candidate key, i.e. just a single field.
 We mark the primary key using \underline{underlining} in visual \glspl{schema}.
 Formally, we write $R(\underline{k : D_k}, a:D_a, b:D_b)$ for a given relation, with all valid instances fulfilling
 \[
-	I \subseteq D_k \times D_a \times D_b \land \forall (k, a, b), (k', a', b') \in I : k = k' \rightarrow (a, b) = (a', b')
+    I \subseteq D_k \times D_a \times D_b \land \forall (k, a, b), (k', a', b') \in I : k = k' \rightarrow (a, b) = (a', b')
 \]
 i.e. if the key is equal, so is the rest of the tuple (thus they are one and the same\footnote{\hlhref{https://www.youtube.com/watch?v=tGeSEbYzhBU}{Heidrun is her name}}).
 

semester4/dmdb/parts/02_theory-background/00_functional-dependencies/04_closure.tex

@@ -1,3 +1,4 @@
+\newpage
 \subsubsection{Closure Algorithm}
 For the definition of the closure, see above.
 

semester4/dmdb/parts/02_theory-background/00_functional-dependencies/06_intuition.tex

@@ -0,0 +1,13 @@
+\subsubsection{Intuition}
+Adapted from the \hlhref{https://en.wikipedia.org/wiki/Functional_dependency}{Wikipedia Article on this topic}
+
+The idea of functional dependencies is to describe which attributes belong to the \textit{determinant set} $X$ and which belong to the \textit{dependent set} $Y$.
+The values of the attributes in the \textit{determinant set} determine the values of $Y$.
+
+Thus, for a relation $R$, with $X, Y \subseteq R$, with $X \rightarrow Y$:
+\begin{itemize}
+    \item When attributes $X$ have known values (let's call them $\bm{x}$),
+          then the values of for their corresponding $Y$ attributes can be determined by looking them up in \bi{any} tuple of $R$ containing the values $\bm{x}$
+    \item Two tuples sharing the same values of $X$ share the same values of $Y$.
+\end{itemize}
+A FD $X \rightarrow Y$ is \textit{trivial}, if $Y \subseteq X$

semester4/dmdb/parts/02_theory-background/01_normal-forms/02_second-nf.tex

@@ -1,4 +1,4 @@
-\subsection{Second Normal Form}
+\subsubsection{Second Normal Form}
 % The two dependencies $\{ \text{Legi}, \text{Nr} \} \rightrightarrow \{ \text{Name}, \text{Semester} \}$,
 % $\{ \text{Legi} \} \rightrightarrow \{ \text{Name}, \text{Semester} \}$ state the following:
 %

semester4/dmdb/parts/02_theory-background/01_normal-forms/07_overview.tex

@@ -0,0 +1,18 @@
+\subsubsection{Overview}
+This overview is adapted from \hlhref{https://en.wikipedia.org/wiki/Database_normalization\#Normal_forms}{this Wikipedia article}.
+All constraint definitions in {\scriptsize smaller font} are informal. Note that \textit{prime attributes} are the attributes that make up a candidate key,
+also known as \textit{key attributes}
+
+\newcommand{\cross}{\ding{55}}
+\begin{tables}{p{10cm}lllll}{Constraint & UNF        & 1NF        & 2NF        & 3NF        & BCNF}
+              Unique rows {\scriptsize (no duplicates)}
+                                        & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\
+              Scalar Columns {\scriptsize (Columns can't contain relations or composite values)}
+                                        & \cross     & \checkmark & \checkmark & \checkmark & \checkmark \\
+              Every non-prime attribute has a full FD on each candidate key {\scriptsize (Attributes depend on the whole of every key)}
+                                        & \cross     & \cross     & \checkmark & \checkmark & \checkmark \\
+              Every Non-trivial FD begins either with superkey or ends with prime attribute {\scriptsize (Attributes depend only on candidate keys)}
+                                        & \cross     & \cross     & \cross     & \checkmark & \checkmark \\
+              Every non-trivial FD begins with a superkey
+                                        & \cross     & \cross     & \cross     & \checkmark & \checkmark \\
+\end{tables}

semester4/dmdb/parts/02_theory-background/main.tex

@@ -7,6 +7,7 @@
 \input{parts/02_theory-background/00_functional-dependencies/03_other-rules.tex}
 \input{parts/02_theory-background/00_functional-dependencies/04_closure.tex}
 \input{parts/02_theory-background/00_functional-dependencies/05_using.tex}
+\input{parts/02_theory-background/00_functional-dependencies/06_intuition.tex}
 % \input{parts/02_theory-background/00_functional-dependencies/}
 
 \input{parts/02_theory-background/01_normal-forms/00_intro.tex}
@@ -16,6 +17,7 @@
 \input{parts/02_theory-background/01_normal-forms/04_bncf.tex}
 \input{parts/02_theory-background/01_normal-forms/05_decomposition-algorithm.tex}
 \input{parts/02_theory-background/01_normal-forms/06_synthesis-algorightm.tex}
+\input{parts/02_theory-background/01_normal-forms/07_overview.tex}
 % \input{parts/02_theory-background/01_normal-forms/}
 
 % \input{parts/02_theory-background/}