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Directory talk:Jon Awbrey/Papers/Differential Propositional Calculus (view source)
Revision as of 14:45, 8 June 2008
, 14:45, 8 June 2008→Appendices @ PlanetMath : TeX Format
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\textbf{Note.} The following Tables are best viewed in the Page Image mode.
\tableofcontents
\subsection{Table A1. Propositional Forms on Two Variables}
\subsection{Table A1. Propositional Forms on Two Variables}
Table A1 lists equivalent expressions for the boolean functions of two variables in a number of different notational systems.
Table A1 lists equivalent expressions for the Boolean functions of two variables in a number of different notational systems.
\begin{quote}\begin{tabular}{|c|c|c|c|c|c|c|}
\begin{quote}\begin{tabular}{|c|c|c|c|c|c|c|}
\subsection{Table A2. Propositional Forms on Two Variables}
\subsection{Table A2. Propositional Forms on Two Variables}
Table A2 lists the sixteen boolean functions of two variables in a different order, grouping them by structural similarity into seven natural classes.
Table A2 lists the sixteen Boolean functions of two variables in a different order, grouping them by structural similarity into seven natural classes.
\begin{quote}\begin{tabular}{|c|c|c|c|c|c|c|}
\begin{quote}\begin{tabular}{|c|c|c|c|c|c|c|}
$f_{15}$ & $((~))$ & $((~))$ & $((~))$ & $((~))$ & $((~))$ \\
$f_{15}$ & $((~))$ & $((~))$ & $((~))$ & $((~))$ & $((~))$ \\
\hline
\hline
\multicolumn{2}{c}{Fixed Point Total:} & 4 & 4 & 4 & 16 \\
\multicolumn{2}{|c||}{\PMlinkname{Fixed Point}{FixedPoint} Total:} & 4 & 4 & 4 & 16 \\
\hline
\end{tabular}\end{quote}
\subsection{Table A4. $\operatorname{D}f$ Expanded Over Differential Features $\{ \operatorname{d}x, \operatorname{d}y \}$}
\begin{quote}\begin{tabular}{|c|c||c|c|c|c|}
\multicolumn{6}{c}{Table A4. $\operatorname{D}f$ Expanded Over Differential Features $\{ \operatorname{d}x, \operatorname{d}y \}$} \\
\hline
& $f$ &
$\operatorname{D}f|_{\operatorname{d}x\ \operatorname{d}y}$ &
$\operatorname{D}f|_{\operatorname{d}x (\operatorname{d}y)}$ &
$\operatorname{D}f|_{(\operatorname{d}x) \operatorname{d}y}$ &
$\operatorname{D}f|_{(\operatorname{d}x)(\operatorname{d}y)}$ \\
\hline
$f_{0}$ & $(~)$ & $(~)$ & $(~)$ & $(~)$ & $(~)$ \\
\hline
$f_{1}$ & $(x)(y)$ & $((x,\ y))$ & $(y)$ & $(x)$ & $(~)$ \\
$f_{2}$ & $(x)\ y$ & $(x,\ y)$ & $y$ & $(x)$ & $(~)$ \\
$f_{4}$ & $x\ (y)$ & $(x,\ y)$ & $(y)$ & $x$ & $(~)$ \\
$f_{8}$ & $x\ y$ & $((x,\ y))$ & $y$ & $x$ & $(~)$ \\
\hline
$f_{3}$ & $(x)$ & $((~))$ & $((~))$ & $(~)$ & $(~)$ \\
$f_{12}$ & $x$ & $((~))$ & $((~))$ & $(~)$ & $(~)$ \\
\hline
$f_{6}$ & $(x,\ y)$ & $(~)$ & $((~))$ & $((~))$ & $(~)$ \\
$f_{9}$ & $((x,\ y))$ & $(~)$ & $((~))$ & $((~))$ & $(~)$ \\
\hline
$f_{5}$ & $(y)$ & $((~))$ & $(~)$ & $((~))$ & $(~)$ \\
$f_{10}$ & $y$ & $((~))$ & $(~)$ & $((~))$ & $(~)$ \\
\hline
$f_{7}$ & $(x\ y)$ & $((x,\ y))$ & $y$ & $x$ & $(~)$ \\
$f_{11}$ & $(x\ (y))$ & $(x,\ y)$ & $(y)$ & $x$ & $(~)$ \\
$f_{13}$ & $((x)\ y)$ & $(x,\ y)$ & $y$ & $(x)$ & $(~)$ \\
$f_{14}$ & $((x)(y))$ & $((x,\ y))$ & $(y)$ & $(x)$ & $(~)$ \\
\hline
$f_{15}$ & $(~)$ & $(~)$ & $(~)$ & $(~)$ & $(~)$ \\
\hline
\hline
\end{tabular}\end{quote}
\end{tabular}\end{quote}