+\clearpage
+\appendix
+\section{Semantics of the Regular Context Language}
+
+\newcommand{\CSEM}[2]{\mathcal{C}\llbracket#1\rrbracket#2}
+\newcommand{\QSEM}[2]{\mathcal{Q}\llbracket#1\rrbracket#2}
+\newcommand{\TSEMUP}[2]{\mathcal{T}^\uparrow\llbracket#1\rrbracket#2}
+\newcommand{\TSEMDOWN}[2]{\mathcal{T}_\downarrow\llbracket#1\rrbracket#2}
+\newcommand{\NSEM}[2]{\mathcal{N}\llbracket#1\rrbracket#2}
+\newcommand{\PSEM}[2]{\mathcal{P}\llbracket#1\rrbracket#2}
+\newcommand{\PPSEM}[2]{\mathcal{P'}\llbracket#1\rrbracket(#2)}
+\newcommand{\PARENT}[1]{\mathit{parent}(#1)}
+\newcommand{\CHILDREN}[1]{\mathit{children}(#1)}
+\newcommand{\ANCESTORS}[1]{\mathit{ancestors}(#1)}
+\newcommand{\DESCENDANTS}[1]{\mathit{descendants}(#1)}
+\newcommand{\HASATTRIBUTE}[2]{\mathit{hasAttribute}(#1,#2)}
+\newcommand{\HASNOATTRIBUTE}[2]{\mathit{hasNoAttribute}(#1,#2)}
+\newcommand{\ATTRIBUTE}[2]{\mathit{attribute}(#1,#2)}
+\newcommand{\ISELEMENT}[1]{\mathit{isElement}(#1)}
+\newcommand{\NAME}[1]{\mathit{name}(#1)}
+\newcommand{\PREV}[1]{\mathit{prev}(#1)}
+\newcommand{\NEXT}[1]{\mathit{next}(#1)}
+
+\[
+\begin{array}{rcl}
+ \CSEM{.}{x} &=& \{x\}\\
+ \CSEM{..}{x} &=& \PARENT{x}\\
+ \CSEM{/}{x} &=& \CHILDREN{x}\\
+ \CSEM{q}{x} &=& \{x_1\mid x_1\in\{x\} \wedge \QSEM{q}{x_1}\}\\
+ \CSEM{(c)}{x} &=& \CSEM{c}{x}\\
+ \CSEM{\alpha(c)}{x} &=& \CSEM{c}{x}, \mbox{bind $\alpha$ to $x$}\\
+ \CSEM{c_1\&c_2}{x} &=& \CSEM{c_1}{x} \cap \CSEM{c_2}{x}\\
+ \CSEM{c_1\mid c_2}{x} &=& \CSEM{c_1}{x} \cup \CSEM{c_2}{x}\\
+ \CSEM{c+}{x} &=& \CSEM{c}{x} \cup \CSEM{c+}{\CSEM{c}{x}}\\
+ \CSEM{c?}{x} &=& \CSEM{.\mid c}{x}\\
+ \CSEM{c*}{x} &=& \CSEM{{c+}?}{x}\\
+ \CSEM{c_1\;c_2}{x} &=& \CSEM{c_2}{\CSEM{c_1}{x}}\\[3ex]
+ \QSEM{\langle*\rangle}{x} &=& \ISELEMENT{x}\\
+ \QSEM{\langle!*\rangle}{x} &=& \neg\QSEM{\langle*\rangle}{x}\\
+ \QSEM{\langle n_1\mid\cdots\mid n_k\rangle}{x} &=& \exists i\in\{1,\dots,k\}:\NAME{x}=n_i\\
+ \QSEM{\langle !n_1\mid\cdots\mid n_k\rangle}{x} &=& \neg\QSEM{\langle n_1\mid\cdots\mid n_k\rangle}{x}\\
+ \QSEM{q[@n]}{x} &=& \QSEM{q}{x} \wedge \HASATTRIBUTE{x}{n}\\
+ \QSEM{q[!@n]}{x} &=& \QSEM{q}{x} \wedge \HASNOATTRIBUTE{x}{n}\\
+ \QSEM{q[@n=v]}{x} &=& \QSEM{q}{x} \wedge \ATTRIBUTE{x}{n}= v\\
+ \QSEM{q[!@n=v]}{x} &=& \QSEM{q}{x} \wedge \ATTRIBUTE{x}{n}\ne v\\
+ \QSEM{q[p]}{x} &=& \QSEM{q}{x} \wedge \PSEM{p}{x}\\
+ \QSEM{q[!p]}{x} &=& \QSEM{q}{x} \wedge \neg\PSEM{p}{x}\\[3ex]
+ \PSEM{p_1\#p_2}{x} &=& \PPSEM{p_1}{*,x}\wedge\PPSEM{p_2}{x,*}\\
+ \PSEM{\cent p_1\#p_2}{x} &=& \PPSEM{p_1}{\cent,x}\wedge\PPSEM{p_2}{x,*}\\
+ \PSEM{p_1\#p_2\$}{x} &=& \PPSEM{p_1}{*,x}\wedge\PPSEM{p_2}{x,\$}\\
+ \PSEM{\cent p_1\#p_2\$}{x} &=& \PPSEM{p_1}{\cent,x}\wedge\PPSEM{p_2}{x,\$}\\[3ex]
+ \PPSEM{}{*,x} &=& \mathit{true}\\
+ \PPSEM{}{\cent,x} &=& \PREV{x}=\emptyset\\
+ \PPSEM{}{x,*} &=& \mathit{true}\\
+ \PPSEM{}{x,\$} &=& \NEXT{x}=\emptyset\\
+ \PPSEM{p\;c}{\alpha,x} &=& \CSEM{c}{\PREV{x}}\ne\emptyset\wedge\PPSEM{p}{\alpha,\PREV{x}}\\
+ \PPSEM{c\;p}{x,\alpha} &=& \CSEM{c}{\NEXT{x}}\ne\emptyset\wedge\PPSEM{p}{\NEXT{x},\alpha}\\
+\end{array}
+\]
+