User:Jon Awbrey/Figures and Tables 1

Format Examples

• \(\rightsquigarrow\)
• \(\leftrightsquigarrow\)
• \(\xrightarrow{\mathrm{Parse}}\)
• \(\xrightarrow[\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~}]{\mathrm{Parse}}\)

Font Size Examples

Medium	\(\text{Algorithmic Translation Rules}\)
Larger	\(\text{Algorithmic Translation Rules}\)
125%	\(\text{Algorithmic Translation Rules}\)
Large	\(\text{Algorithmic Translation Rules}\)
150%	\(\text{Algorithmic Translation Rules}\)

Algorithmic Translation Rules

PNG

\(\text{Algorithmic Translation Rules}\)

LaTeX

\(\text{Algorithmic Translation Rules}\)

\(\text{Sentence in PARCE}\) \(\xrightarrow{\mathrm{Parse}}\) \(\text{Graph in PARC}\)

\(\mathrm{Conc}^0\) \(\xrightarrow{\mathrm{Parse}}\) \(\mathrm{Node}^0\) \(\mathrm{Conc}_{j=1}^k s_j\) \(\xrightarrow{\mathrm{Parse}}\) \(\mathrm{Node}_{j=1}^k \mathrm{Parse} (s_j)\)

\(\mathrm{Surc}^0\) \(\xrightarrow{\mathrm{Parse}}\) \(\mathrm{Lobe}^0\) \(\mathrm{Surc}_{j=1}^k s_j\) \(\xrightarrow{\mathrm{Parse}}\) \(\mathrm{Lobe}_{j=1}^k \mathrm{Parse} (s_j)\)

Semantic Translation • Functional Form

PNG

\(\text{Semantic Translation}\) • \(\text{Functional Form}\)

LaTeX

\(\text{Semantic Translation}\) • \(\text{Functional Form}\)

\(\mathrm{Sentence}\) \(\xrightarrow[\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}]{\mathrm{Parse}}\) \(\mathrm{Graph}\) \(\xrightarrow[\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}]{\mathrm{Denotation}}\) \(\mathrm{Proposition}\)

\(s_j\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(C_j\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(q_j\)

\(\mathrm{Conc}^0\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(\mathrm{Node}^0\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(1\) \(\mathrm{Conc}^k_j s_j\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(\mathrm{Node}^k_j C_j\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(\mathrm{Conj}^k_j q_j\)

\(\mathrm{Surc}^0\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(\mathrm{Lobe}^0\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(0\) \(\mathrm{Surc}^k_j s_j\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(\mathrm{Lobe}^k_j C_j\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(\mathrm{Surj}^k_j q_j\)

Semantic Translation • Equational Form

PNG

\(\text{Semantic Translation}\) • \(\text{Equational Form}\)

LaTeX

\(\text{Semantic Translation}\) • \(\text{Equational Form}\)

\(\downharpoonleft \mathrm{Sentence} \downharpoonright\) \(\stackrel{\mathrm{Parse}}{=}\) \(\downharpoonleft \mathrm{Graph} \downharpoonright\) \(\stackrel{\mathrm{Denotation}}{=}\) \(\mathrm{Proposition}\)

\(\downharpoonleft s_j \downharpoonright\) \(=\) \(\downharpoonleft C_j \downharpoonright\) \(=\) \(q_j\)

\(\downharpoonleft \mathrm{Conc}^0 \downharpoonright\) \(=\) \(\downharpoonleft \mathrm{Node}^0 \downharpoonright\) \(=\) \(1\) \(\downharpoonleft \mathrm{Conc}^k_j s_j \downharpoonright\) \(=\) \(\downharpoonleft \mathrm{Node}^k_j C_j \downharpoonright\) \(=\) \(\mathrm{Conj}^k_j q_j\)

\(\downharpoonleft \mathrm{Surc}^0 \downharpoonright\) \(=\) \(\downharpoonleft \mathrm{Lobe}^0 \downharpoonright\) \(=\) \(0\) \(\downharpoonleft \mathrm{Surc}^k_j s_j \downharpoonright\) \(=\) \(\downharpoonleft \mathrm{Lobe}^k_j C_j \downharpoonright\) \(=\) \(\mathrm{Surj}^k_j q_j\)

Boolean Functions on Zero Variables

LaTeX

\(\text{Boolean Functions on Zero Variables}\)

\(F\)	\(F\)	\(F()\)	\(F\)
\(0\)	\(F_0^{(0)}\)	\(0\)	\(\texttt{( )}\)
\(1\)	\(F_1^{(0)}\)	\(1\)	\(\texttt{(( ))}\)

Boolean Functions on One Variable

LaTeX

\(\text{Boolean Functions on One Variable}\)

\(F\)	\(F\)	\(F(x)\)		\(F\)
		\(F(1)\)	\(F(0)\)
\(F_0^{(1)}\)	\(F_{00}^{(1)}\)	\(0\)	\(0\)	\(\texttt{( )}\)
\(F_1^{(1)}\)	\(F_{01}^{(1)}\)	\(0\)	\(1\)	\(\texttt{(} x \texttt{)}\)
\(F_2^{(1)}\)	\(F_{10}^{(1)}\)	\(1\)	\(0\)	\(x\)
\(F_3^{(1)}\)	\(F_{11}^{(1)}\)	\(1\)	\(1\)	\(\texttt{(( ))}\)

Boolean Functions on Two Variables

LaTeX

\(\text{Boolean Functions on Two Variables}\)

\(F\)	\(F\)	\(F(x, y)\)				\(F\)
		\(F(1, 1)\)	\(F(1, 0)\)	\(F(0, 1)\)	\(F(0, 0)\)
\(F_{0}^{(2)}\)	\(F_{0000}^{(2)}\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\texttt{( )}\)
\(F_{1}^{(2)}\)	\(F_{0001}^{(2)}\)	\(0\)	\(0\)	\(0\)	\(1\)	\(\texttt{(} x \texttt{)(} y \texttt{)}\)
\(F_{2}^{(2)}\)	\(F_{0010}^{(2)}\)	\(0\)	\(0\)	\(1\)	\(0\)	\(\texttt{(} x \texttt{)} y\)
\(F_{3}^{(2)}\)	\(F_{0011}^{(2)}\)	\(0\)	\(0\)	\(1\)	\(1\)	\(\texttt{(} x \texttt{)}\)
\(F_{4}^{(2)}\)	\(F_{0100}^{(2)}\)	\(0\)	\(1\)	\(0\)	\(0\)	\(x \texttt{(} y \texttt{)}\)
\(F_{5}^{(2)}\)	\(F_{0101}^{(2)}\)	\(0\)	\(1\)	\(0\)	\(1\)	\(\texttt{(} y \texttt{)}\)
\(F_{6}^{(2)}\)	\(F_{0110}^{(2)}\)	\(0\)	\(1\)	\(1\)	\(0\)	\(\texttt{(} x \texttt{,} y \texttt{)}\)
\(F_{7}^{(2)}\)	\(F_{0111}^{(2)}\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\texttt{(} x y \texttt{)}\)
\(F_{8}^{(2)}\)	\(F_{1000}^{(2)}\)	\(1\)	\(0\)	\(0\)	\(0\)	\(x y\)
\(F_{9}^{(2)}\)	\(F_{1001}^{(2)}\)	\(1\)	\(0\)	\(0\)	\(1\)	\(\texttt{((} x \texttt{,} y \texttt{))}\)
\(F_{10}^{(2)}\)	\(F_{1010}^{(2)}\)	\(1\)	\(0\)	\(1\)	\(0\)	\(y\)
\(F_{11}^{(2)}\)	\(F_{1011}^{(2)}\)	\(1\)	\(0\)	\(1\)	\(1\)	\(\texttt{(} x \texttt{(} y \texttt{))}\)
\(F_{12}^{(2)}\)	\(F_{1100}^{(2)}\)	\(1\)	\(1\)	\(0\)	\(0\)	\(x\)
\(F_{13}^{(2)}\)	\(F_{1101}^{(2)}\)	\(1\)	\(1\)	\(0\)	\(1\)	\(\texttt{((} x \texttt{)} y \texttt{)}\)
\(F_{14}^{(2)}\)	\(F_{1110}^{(2)}\)	\(1\)	\(1\)	\(1\)	\(0\)	\(\texttt{((} x \texttt{)(} y \texttt{))}\)
\(F_{15}^{(2)}\)	\(F_{1111}^{(2)}\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\texttt{(( ))}\)