+\[
+\begin{array}{rcl}
+ \PSEM{q} &=& \FUN{x}{\APPLY{\QSEM{q}{}}{x}} \\
+ \PSEM{..} &=& \FUN{x}{\neg\APPLY{\mathit{null}}{\PARENT{x}}}\\
+ \PSEM{/} &=& \FUN{x}{\neg\APPLY{\mathit{null}}{\CHILD{x}}}\\
+ \PSEM{(c)} &=& \PSEM{c}\\
+ \PSEM{\{c:\alpha\}} &=& \FUN{x}{\APPLY{\PSEM{c}}{x}\AAND\APPLY{\alpha}{x}}\\
+ \PSEM{c_1\;c_2} &=& \IFV{\PREDICATE{c_1}}{\FUN{x}{(\PSEM{c_1}\;x)\wedge(\PSEM{c_2}\;x)}}{\FSEM{c_1}{\PSEM{c_2},\FUN{\_}{\FALSE}}}\\
+ \PSEM{c_1\&c_2} &=& \IFV{\PREDICATE{c_1}\wedge\PREDICATE{c_2}}{\FUN{x}{(\PSEM{c_1}\;x)\wedge(\PSEM{c_2}\;x)}}{\FSEM{c_1\&c_2}{\FUN{\_}{\TRUE},\FUN{\_}{\FALSE}}}\\
+ \PSEM{c_1\mid c_2} &=& \FUN{x}{(\PSEM{c_1}\;x)\vee(\PSEM{c_2}\;x)}\\
+ \PSEM{c+} &=& \PSEM{c}\\
+ \PSEM{c?} &=& \FUN{\_}{\TRUE}\\
+ \PSEM{c*} &=& \FUN{\_}{\TRUE}\\[3ex]
+ \FSEM{q}{t,f} &=& \FUN{x}{(\APPLY{\PSEM{q}}{x}\AAND\APPLY{t}{x})\AOR\APPLY{f}{x}}\\
+ \FSEM{..}{t,f} &=& \FUN{x}{\MATCH{\PARENT{x}}{y}{\APPLY{t}{y}}{\APPLY{f}{x}}}\\
+% \FSEM{/}{t,f} &=& \FUN{x}{(\vee_{y\in\CHILDREN{x}} \APPLY{t}{y})\AOR\APPLY{f}{x}}\\
+ \FSEM{/}{t,f} &=& \FUN{x}{\APPLYX{\mathit{exists}}{t}{\CHILD{x}}\AOR\APPLY{f}{x}}\\
+ \FSEM{(c)}{t,f} &=& \FSEM{c}{t,f}\\
+ \FSEM{\{c:\alpha\}}{t,f} &=& \FSEM{c}{\FUN{x}{\PSEM{c}\AAND\APPLY{\alpha}{x}\AAND\APPLY{t}{x},f}}\\
+ \FSEM{c_1\;c_2}{t,f} &=& \FUN{x}{\APPLY{\FSEM{c_1}{\FSEM{c_2}{t,\FUN{\_}{\APPLY{f}{x}}},f}}{x}}\\
+ \FSEM{c_1\&c_2}{t,f} &=& \FUN{x}{\APPLY{\FSEM{c_1}{\FUN{y}{\APPLY{\FSEM{c_2}{\FUN{z}{(y=z)\AAND\APPLY{t}{z}},\FUN{\_}{\APPLY{f}{x}}}}{x}},f}}{x}}\\
+ \FSEM{c_1\mid c_2}{t,f} &=& \FSEM{c_1}{t,\FSEM{c_2}{t,f}}\\
+ \FSEM{c+}{t,f} &=& \FSEM{c}{\FSEM{c+}{t,t},f}\\
+ \FSEM{c?}{t,f} &=& \FSEM{c}{t,t}\\
+ \FSEM{c*}{t,f} &=& \FSEM{{c+}?}{t,f}\\[3ex]
+ \QSEM{c}{} &=& \PSEM{c}\\
+ \QSEM{!c}{} &=& \FUN{x}{\neg\APPLY{\PSEM{c}}{x}}\\
+ \QSEM{\langle*\rangle}{} &=& \FUN{\_}{\TRUE}\\
+ \QSEM{\langle n\rangle}{} &=& \FUN{x}{\NAME{x}=n}\\
+ \QSEM{@n}{} &=& \FUN{x}{\HASATTRIBUTE{x}{n}}\\
+ \QSEM{@n=v}{} &=& \FUN{x}{\ATTRIBUTE{x}{n}=v}\\
+ \QSEM{[p_1\#p_2]}{} &=& \FUN{x}{\APPLY{\LSEM{p_1}{}}{\PREV{x}}\wedge\APPLY{\RSEM{p_2}{}}{\NEXT{x}}}\\[3ex]
+ \LSEM{}{} &=& \FUN{\_}{\TRUE}\\
+ \LSEM{\cent}{} &=& \mathit{null}\\
+ \LSEM{p\;q}{} &=& \FUN{x}{\MATCH{x}{y}{\QSEM{q}{y}\AAND\APPLY{\LSEM{p}}{\PREV{y}}}{\FALSE}}\\
+ \RSEM{}{} &=& \FUN{\_}{\TRUE}\\
+ \RSEM{\$}{} &=& \mathit{null}\\
+ \RSEM{p\;q}{} &=& \FUN{x}{\MATCH{x}{y}{\QSEM{q}{y}\AAND\APPLY{\RSEM{p}}{\NEXT{y}}}{\FALSE}}\\
+ \mathit{null} &=& \FUN{x}{\MATCH{x}{\_}{\FALSE}{\TRUE}}\\
+ \mathit{exists} &=& \FUN{t}{\REC{a}{\FUN{x}{\MATCH{x}{y}{\APPLY{t}{y}\AOR\APPLY{a}{\NEXT{x}}}{\FALSE}}}}
+\end{array}
+\]
+
+
+