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

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(→‎Format Samples: + <math>\xrightarrow[\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}]{\mathrm{Parse}}</math>)
(+ Table 16. Boolean Functions on Zero Variables)
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| width="20%" | <math>\mathrm{Surj}^k_j q_j</math>
 
| width="20%" | <math>\mathrm{Surj}^k_j q_j</math>
 
|}
 
|}
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|}
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<br>
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==Table 16. Boolean Functions on Zero Variables==
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<br>
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:60%"
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|+ style="height:30px" | <math>\text{Table 16. Boolean Functions on Zero Variables}</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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| width="48%" | <math>F()</math>
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| width="24%" | <math>F</math>
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|-
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| <math>0</math>
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| <math>F_0^{(0)}</math>
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| <math>0</math>
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| <math>\texttt{( )}</math>
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|-
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| <math>1</math>
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| <math>F_1^{(0)}</math>
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| <math>1</math>
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| <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


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


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