Difference between revisions of "User:Jon Awbrey/Figures and Tables 1"

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(+ Table 16. Boolean Functions on Zero Variables)
(+ Table 17. Boolean Functions on One Variable)
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| <math>1</math>
 
| <math>1</math>
 
| <math>F_1^{(0)}</math>
 
| <math>F_1^{(0)}</math>
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| <math>1</math>
 +
| <math>\texttt{(( ))}</math>
 +
|}
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 +
<br>
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 +
==Table 17. Boolean Functions on One Variable==
 +
 +
<br>
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 +
{| align="center" border="1" cellpadding="6" cellspacing="0" style="text-align:center; width:60%"
 +
|+ style="height:30px" | <math>\text{Table 17. Boolean Functions on One Variable}</math>
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|- style="height:40px; background:ghostwhite"
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| width="14%" | <math>F</math>
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| width="14%" | <math>F</math>
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| colspan="2" | <math>F(x)</math>
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| width="24%" | <math>F</math>
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|- style="height:40px; background:ghostwhite"
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| width="14%" | &nbsp;
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| width="14%" | &nbsp;
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| width="24%" | <math>F(1)</math>
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| width="24%" | <math>F(0)</math>
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| width="24%" | &nbsp;
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|-
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| <math>F_0^{(1)}</math>
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| <math>F_{00}^{(1)}</math>
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| <math>0</math>
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| <math>0</math>
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| <math>\texttt{( )}</math>
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|-
 +
| <math>F_1^{(1)}</math>
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| <math>F_{01}^{(1)}</math>
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| <math>0</math>
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| <math>1</math>
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| <math>\texttt{(} x \texttt{)}</math>
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|-
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| <math>F_2^{(1)}</math>
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| <math>F_{10}^{(1)}</math>
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| <math>1</math>
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| <math>0</math>
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| <math>x</math>
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|-
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| <math>F_3^{(1)}</math>
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| <math>F_{11}^{(1)}</math>
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| <math>1</math>
 
| <math>1</math>
 
| <math>1</math>
 
| <math>\texttt{(( ))}</math>
 
| <math>\texttt{(( ))}</math>

Revision as of 19:15, 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


\(\text{Table 16. Boolean Functions on Zero Variables}\)
\(F\) \(F\) \(F()\) \(F\)
\(0\) \(F_0^{(0)}\) \(0\) \(\texttt{( )}\)
\(1\) \(F_1^{(0)}\) \(1\) \(\texttt{(( ))}\)


Table 17. Boolean Functions on One Variable


\(\text{Table 17. Boolean Functions on One Variable}\)
\(F\) \(F\) \(F(x)\) \(F\)
    \(F(1)\) \(F(0)\)  
\(F_0^{(1)}\) \(F_{00}^{(1)}\) \(0\) \(0\) \(\texttt{( )}\)
\(F_1^{(1)}\) \(F_{01}^{(1)}\) \(0\) \(1\) \(\texttt{(} x \texttt{)}\)
\(F_2^{(1)}\) \(F_{10}^{(1)}\) \(1\) \(0\) \(x\)
\(F_3^{(1)}\) \(F_{11}^{(1)}\) \(1\) \(1\) \(\texttt{(( ))}\)


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