User:Jon Awbrey/Figures and Tables 1

Format Samples

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

Table 14. Semantic Translation • Functional Form

\(\text{Table 14. Semantic Translation : Functional Form}\)

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

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

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

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

Table 15. Semantic Translation • Equational Form

\(\text{Table 15. Semantic Translation : Equational Form}\)

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

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

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

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

Table 16. Boolean Functions on Zero Variables

\(\text{Table 16. Boolean Functions on Zero Variables}\)

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

Table 17. Boolean Functions on One Variable

\(\text{Table 17. Boolean Functions on One Variable}\)

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