MyWikiBiz, Author Your Legacy — Sunday March 08, 2026
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| | | width="20%" | <math>\mathrm{Surj}^k_j q_j</math> | | | width="20%" | <math>\mathrm{Surj}^k_j q_j</math> |
| | |} | | |} |
| | + | |} |
| | + | |
| | + | <br> |
| | + | |
| | + | ==Table 16. Boolean Functions on Zero Variables== |
| | + | |
| | + | <br> |
| | + | |
| | + | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:60%" |
| | + | |+ style="height:30px" | <math>\text{Table 16. Boolean Functions on Zero Variables}</math> |
| | + | |- style="height:40px; background:ghostwhite" |
| | + | | width="14%" | <math>F</math> |
| | + | | width="14%" | <math>F</math> |
| | + | | width="48%" | <math>F()</math> |
| | + | | width="24%" | <math>F</math> |
| | + | |- |
| | + | | <math>0</math> |
| | + | | <math>F_0^{(0)}</math> |
| | + | | <math>0</math> |
| | + | | <math>\texttt{( )}</math> |
| | + | |- |
| | + | | <math>1</math> |
| | + | | <math>F_1^{(0)}</math> |
| | + | | <math>1</math> |
| | + | | <math>\texttt{(( ))}</math> |
| | |} | | |} |
| | | | |
| | <br> | | <br> |
Revision as of 19:12, 17 October 2025
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
\(\text{Table 16. Boolean Functions on Zero Variables}\)
| \(F\)
|
\(F\)
|
\(F()\)
|
\(F\)
|
| \(0\)
|
\(F_0^{(0)}\)
|
\(0\)
|
\(\texttt{( )}\)
|
| \(1\)
|
\(F_1^{(0)}\)
|
\(1\)
|
\(\texttt{(( ))}\)
|
