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

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(+ <math>\xrightarrow{\mathrm{Parse}}</math> + <math>\leftrightsquigarrow</math>)
(+ Table 14. Semantic Translation • Functional Form + Table 15. Semantic Translation • Equational Form)
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==Format Samples==
  
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* <math>\rightsquigarrow</math>
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* <math>\leftrightsquigarrow</math>
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* <math>\xrightarrow{\mathrm{Parse}}</math>
  
−
<math>\xrightarrow{\mathrm{Parse}}</math>
+
==Table 14. Semantic Translation &bull; Functional Form==
  
−
<math>\rightsquigarrow</math>
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:60%"
 +
|+ style="height:30px" | <math>\text{Table 14. Semantic Translation : Functional Form}</math>
 +
|- style="height:40px; background:ghostwhite"
 +
|
 +
{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:ghostwhite; width:100%"
 +
| width="20%" | <math>\mathrm{Sentence}</math>
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| width="20%" | <math>\xrightarrow[\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}]{\mathrm{Parse}}</math>
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| width="20%" | <math>\mathrm{Graph}</math>
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| width="20%" | <math>\xrightarrow[\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}]{\mathrm{Denotation}}</math>
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| width="20%" | <math>\mathrm{Proposition}</math>
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|}
 +
|-
 +
|
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{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
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| width="20%" | <math>s_j</math>
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| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
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| width="20%" | <math>C_j</math>
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| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
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| width="20%" | <math>q_j</math>
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|}
 +
|-
 +
|
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{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
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| width="20%" | <math>\mathrm{Conc}^0</math>
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| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
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| width="20%" | <math>\mathrm{Node}^0</math>
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| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
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| width="20%" | <math>1</math>
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|-
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| width="20%" | <math>\mathrm{Conc}^k_j s_j</math>
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| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
 +
| width="20%" | <math>\mathrm{Node}^k_j C_j</math>
 +
| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
 +
| width="20%" | <math>\mathrm{Conj}^k_j q_j</math>
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|}
 +
|-
 +
|
 +
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
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| width="20%" | <math>\mathrm{Surc}^0</math>
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| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
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| width="20%" | <math>\mathrm{Lobe}^0</math>
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| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
 +
| width="20%" | <math>0</math>
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|-
 +
| width="20%" | <math>\mathrm{Surc}^k_j s_j</math>
 +
| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
 +
| width="20%" | <math>\mathrm{Lobe}^k_j C_j</math>
 +
| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
 +
| width="20%" | <math>\mathrm{Surj}^k_j q_j</math>
 +
|}
 +
|}
  
−
<math>\leftrightsquigarrow</math>
+
==Table 15. Semantic Translation &bull; Equational Form==
 +
 
 +
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:60%"
 +
|+ style="height:30px" | <math>\text{Table 15. Semantic Translation : Equational Form}</math>
 +
|- style="height:40px; background:ghostwhite"
 +
|
 +
{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:ghostwhite; width:100%"
 +
| width="20%" | <math>\downharpoonleft \mathrm{Sentence} \downharpoonright</math>
 +
| width="20%" | <math>\stackrel{\mathrm{Parse}}{=}</math>
 +
| width="20%" | <math>\downharpoonleft \mathrm{Graph} \downharpoonright</math>
 +
| width="20%" | <math>\stackrel{\mathrm{Denotation}}{=}</math>
 +
| width="20%" | <math>\mathrm{Proposition}</math>
 +
|}
 +
|-
 +
|
 +
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
 +
| width="20%" | <math>\downharpoonleft s_j \downharpoonright</math>
 +
| width="20%" | <math>=</math>
 +
| width="20%" | <math>\downharpoonleft C_j \downharpoonright</math>
 +
| width="20%" | <math>=</math>
 +
| width="20%" | <math>q_j</math>
 +
|}
 +
|-
 +
|
 +
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
 +
| width="20%" | <math>\downharpoonleft \mathrm{Conc}^0 \downharpoonright</math>
 +
| width="20%" | <math>=</math>
 +
| width="20%" | <math>\downharpoonleft \mathrm{Node}^0 \downharpoonright</math>
 +
| width="20%" | <math>=</math>
 +
| width="20%" | <math>1</math>
 +
|-
 +
| width="20%" | <math>\downharpoonleft \mathrm{Conc}^k_j s_j \downharpoonright</math>
 +
| width="20%" | <math>=</math>
 +
| width="20%" | <math>\downharpoonleft \mathrm{Node}^k_j C_j \downharpoonright</math>
 +
| width="20%" | <math>=</math>
 +
| width="20%" | <math>\mathrm{Conj}^k_j q_j</math>
 +
|}
 +
|-
 +
|
 +
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
 +
| width="20%" | <math>\downharpoonleft \mathrm{Surc}^0 \downharpoonright</math>
 +
| width="20%" | <math>=</math>
 +
| width="20%" | <math>\downharpoonleft \mathrm{Lobe}^0 \downharpoonright</math>
 +
| width="20%" | <math>=</math>
 +
| width="20%" | <math>0</math>
 +
|-
 +
| width="20%" | <math>\downharpoonleft \mathrm{Surc}^k_j s_j \downharpoonright</math>
 +
| width="20%" | <math>=</math>
 +
| width="20%" | <math>\downharpoonleft \mathrm{Lobe}^k_j C_j \downharpoonright</math>
 +
| width="20%" | <math>=</math>
 +
| width="20%" | <math>\mathrm{Surj}^k_j q_j</math>
 +
|}
 +
|}
 +
 
 +
<br>

Revision as of 19:00, 17 October 2025

Format Samples

  • \(\rightsquigarrow\)
  • \(\leftrightsquigarrow\)
  • \(\xrightarrow{\mathrm{Parse}}\)

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

\(\text{Table 15. Semantic Translation : Equational Form}\)
\(\downharpoonleft \mathrm{Sentence} \downharpoonright\) \(\stackrel{\mathrm{Parse}}{=}\) \(\downharpoonleft \mathrm{Graph} \downharpoonright\) \(\stackrel{\mathrm{Denotation}}{=}\) \(\mathrm{Proposition}\)
\(\downharpoonleft s_j \downharpoonright\) \(=\) \(\downharpoonleft C_j \downharpoonright\) \(=\) \(q_j\)
\(\downharpoonleft \mathrm{Conc}^0 \downharpoonright\) \(=\) \(\downharpoonleft \mathrm{Node}^0 \downharpoonright\) \(=\) \(1\)
\(\downharpoonleft \mathrm{Conc}^k_j s_j \downharpoonright\) \(=\) \(\downharpoonleft \mathrm{Node}^k_j C_j \downharpoonright\) \(=\) \(\mathrm{Conj}^k_j q_j\)
\(\downharpoonleft \mathrm{Surc}^0 \downharpoonright\) \(=\) \(\downharpoonleft \mathrm{Lobe}^0 \downharpoonright\) \(=\) \(0\)
\(\downharpoonleft \mathrm{Surc}^k_j s_j \downharpoonright\) \(=\) \(\downharpoonleft \mathrm{Lobe}^k_j C_j \downharpoonright\) \(=\) \(\mathrm{Surj}^k_j q_j\)


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