MyWikiBiz, Author Your Legacy — Saturday October 18, 2025
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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
\(\text{Table 17. Boolean Functions on One Variable}\)
| \(F\)
|
\(F\)
|
\(F(x)\)
|
\(F\)
|
|
|
|
\(F(1)\)
|
\(F(0)\)
|
|
| \(F_0^{(1)}\)
|
\(F_{00}^{(1)}\)
|
\(0\)
|
\(0\)
|
\(\texttt{( )}\)
|
| \(F_1^{(1)}\)
|
\(F_{01}^{(1)}\)
|
\(0\)
|
\(1\)
|
\(\texttt{(} x \texttt{)}\)
|
| \(F_2^{(1)}\)
|
\(F_{10}^{(1)}\)
|
\(1\)
|
\(0\)
|
\(x\)
|
| \(F_3^{(1)}\)
|
\(F_{11}^{(1)}\)
|
\(1\)
|
\(1\)
|
\(\texttt{(( ))}\)
|
