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
\(\text{Table 17. Boolean Functions on One Variable}\)
| \(F\)
|
\(F\)
|
\(F(x)\)
|
\(F\)
|
|
|
|
\(F(1)\)
|
\(F(0)\)
|
|
| \(F_0^{(1)}\)
|
\(F_{00}^{(1)}\)
|
\(0\)
|
\(0\)
|
\(\texttt{( )}\)
|
| \(F_1^{(1)}\)
|
\(F_{01}^{(1)}\)
|
\(0\)
|
\(1\)
|
\(\texttt{(} x \texttt{)}\)
|
| \(F_2^{(1)}\)
|
\(F_{10}^{(1)}\)
|
\(1\)
|
\(0\)
|
\(x\)
|
| \(F_3^{(1)}\)
|
\(F_{11}^{(1)}\)
|
\(1\)
|
\(1\)
|
\(\texttt{(( ))}\)
|
Table 18. Boolean Functions on Two Variables
\(\text{Table 18. Boolean Functions on Two Variables}\)
| \(F\)
|
\(F\)
|
\(F(x, y)\)
|
\(F\)
|
|
|
|
\(F(1, 1)\)
|
\(F(1, 0)\)
|
\(F(0, 1)\)
|
\(F(0, 0)\)
|
|
| \(F_{0}^{(2)}\)
|
\(F_{0000}^{(2)}\)
|
\(0\)
|
\(0\)
|
\(0\)
|
\(0\)
|
\(\texttt{( )}\)
|
| \(F_{1}^{(2)}\)
|
\(F_{0001}^{(2)}\)
|
\(0\)
|
\(0\)
|
\(0\)
|
\(1\)
|
\(\texttt{(} x \texttt{)(} y \texttt{)}\)
|
| \(F_{2}^{(2)}\)
|
\(F_{0010}^{(2)}\)
|
\(0\)
|
\(0\)
|
\(1\)
|
\(0\)
|
\(\texttt{(} x \texttt{)} y\)
|
| \(F_{3}^{(2)}\)
|
\(F_{0011}^{(2)}\)
|
\(0\)
|
\(0\)
|
\(1\)
|
\(1\)
|
\(\texttt{(} x \texttt{)}\)
|
| \(F_{4}^{(2)}\)
|
\(F_{0100}^{(2)}\)
|
\(0\)
|
\(1\)
|
\(0\)
|
\(0\)
|
\(x \texttt{(} y \texttt{)}\)
|
| \(F_{5}^{(2)}\)
|
\(F_{0101}^{(2)}\)
|
\(0\)
|
\(1\)
|
\(0\)
|
\(1\)
|
\(\texttt{(} y \texttt{)}\)
|
| \(F_{6}^{(2)}\)
|
\(F_{0110}^{(2)}\)
|
\(0\)
|
\(1\)
|
\(1\)
|
\(0\)
|
\(\texttt{(} x \texttt{,} y \texttt{)}\)
|
| \(F_{7}^{(2)}\)
|
\(F_{0111}^{(2)}\)
|
\(0\)
|
\(1\)
|
\(1\)
|
\(1\)
|
\(\texttt{(} x y \texttt{)}\)
|
| \(F_{8}^{(2)}\)
|
\(F_{1000}^{(2)}\)
|
\(1\)
|
\(0\)
|
\(0\)
|
\(0\)
|
\(x y\)
|
| \(F_{9}^{(2)}\)
|
\(F_{1001}^{(2)}\)
|
\(1\)
|
\(0\)
|
\(0\)
|
\(1\)
|
\(\texttt{((} x \texttt{,} y \texttt{))}\)
|
| \(F_{10}^{(2)}\)
|
\(F_{1010}^{(2)}\)
|
\(1\)
|
\(0\)
|
\(1\)
|
\(0\)
|
\(y\)
|
| \(F_{11}^{(2)}\)
|
\(F_{1011}^{(2)}\)
|
\(1\)
|
\(0\)
|
\(1\)
|
\(1\)
|
\(\texttt{(} x \texttt{(} y \texttt{))}\)
|
| \(F_{12}^{(2)}\)
|
\(F_{1100}^{(2)}\)
|
\(1\)
|
\(1\)
|
\(0\)
|
\(0\)
|
\(x\)
|
| \(F_{13}^{(2)}\)
|
\(F_{1101}^{(2)}\)
|
\(1\)
|
\(1\)
|
\(0\)
|
\(1\)
|
\(\texttt{((} x \texttt{)} y \texttt{)}\)
|
| \(F_{14}^{(2)}\)
|
\(F_{1110}^{(2)}\)
|
\(1\)
|
\(1\)
|
\(1\)
|
\(0\)
|
\(\texttt{((} x \texttt{)(} y \texttt{))}\)
|
| \(F_{15}^{(2)}\)
|
\(F_{1111}^{(2)}\)
|
\(1\)
|
\(1\)
|
\(1\)
|
\(1\)
|
\(\texttt{(( ))}\)
|
