Difference between revisions of "User:Jon Awbrey/SANDBOX"

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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
 
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
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|+ '''Table 14.1 Semantic Translation : Functional Form'''
+
|+ '''Table 14.2 Semantic Translation : Equational Form'''
 
|- style="background:whitesmoke"
 
|- style="background:whitesmoke"
 
|
 
|
 
{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:whitesmoke; width:100%"
 
{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:whitesmoke; width:100%"
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| width="20%" | <math>\operatorname{Sentence}</math>
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| width="20%" | <math>\downharpoonleft \operatorname{Sentence} \downharpoonright</math>
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| width="20%" | <math>\xrightarrow[\operatorname{~~~~~~~~~~}]{\operatorname{Parse}}</math>
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| width="20%" | <math>\stackrel{\operatorname{Parse}}{=}</math>
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| width="20%" | <math>\operatorname{Graph}</math>
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| width="20%" | <math>\downharpoonleft \operatorname{Graph} \downharpoonright</math>
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| width="20%" | <math>\xrightarrow[\operatorname{~~~~~~~~~~}]{\operatorname{Denotation}}</math>
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| width="20%" | <math>\stackrel{\operatorname{Denotation}}{=}</math>
 
| width="20%" | <math>\operatorname{Proposition}</math>
 
| width="20%" | <math>\operatorname{Proposition}</math>
 
|}
 
|}
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|
 
|
 
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
 
{| 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>\downharpoonleft s_j \downharpoonright</math>
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| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
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| width="20%" | <math>=\!</math>
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| width="20%" | <math>C_j\!</math>
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| width="20%" | <math>\downharpoonleft C_j \downharpoonright</math>
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| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
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| width="20%" | <math>=\!</math>
 
| width="20%" | <math>q_j\!</math>
 
| width="20%" | <math>q_j\!</math>
 
|}
 
|}
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|
 
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
 
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
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| width="20%" | <math>\operatorname{Conc}^0</math>
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| width="20%" | <math>\downharpoonleft \operatorname{Conc}^0 \downharpoonright</math>
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| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
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| width="20%" | <math>=\!</math>
−
| width="20%" | <math>\operatorname{Node}^0</math>
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| width="20%" | <math>\downharpoonleft \operatorname{Node}^0 \downharpoonright</math>
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| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
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| width="20%" | <math>=\!</math>
 
| width="20%" | <math>\underline{1}</math>
 
| width="20%" | <math>\underline{1}</math>
 
|-
 
|-
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| width="20%" | <math>\operatorname{Conc}^k_j s_j</math>
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| width="20%" | <math>\downharpoonleft \operatorname{Conc}^k_j s_j \downharpoonright</math>
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| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
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| width="20%" | <math>=\!</math>
−
| width="20%" | <math>\operatorname{Node}^k_j C_j</math>
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| width="20%" | <math>\downharpoonleft \operatorname{Node}^k_j C_j \downharpoonright</math>
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| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
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| width="20%" | <math>=\!</math>
 
| width="20%" | <math>\operatorname{Conj}^k_j q_j</math>
 
| width="20%" | <math>\operatorname{Conj}^k_j q_j</math>
 
|}
 
|}
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|
 
|
 
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
 
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
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| width="20%" | <math>\operatorname{Surc}^0</math>
+
| width="20%" | <math>\downharpoonleft \operatorname{Surc}^0 \downharpoonright</math>
−
| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
+
| width="20%" | <math>=\!</math>
−
| width="20%" | <math>\operatorname{Lobe}^0</math>
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| width="20%" | <math>\downharpoonleft \operatorname{Lobe}^0 \downharpoonright</math>
−
| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
+
| width="20%" | <math>=\!</math>
 
| width="20%" | <math>\underline{0}</math>
 
| width="20%" | <math>\underline{0}</math>
 
|-
 
|-
−
| width="20%" | <math>\operatorname{Surc}^k_j s_j</math>
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| width="20%" | <math>\downharpoonleft \operatorname{Surc}^k_j s_j \downharpoonright</math>
−
| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
+
| width="20%" | <math>=\!</math>
−
| width="20%" | <math>\operatorname{Lobe}^k_j C_j</math>
+
| width="20%" | <math>\downharpoonleft \operatorname{Lobe}^k_j C_j \downharpoonright</math>
−
| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
+
| width="20%" | <math>=\!</math>
 
| width="20%" | <math>\operatorname{Surj}^k_j q_j</math>
 
| width="20%" | <math>\operatorname{Surj}^k_j q_j</math>
 
|}
 
|}

Revision as of 13:00, 22 January 2009

Grammar Stuff


Table 13. Algorithmic Translation Rules
\(\text{Sentence in PARCE}\!\) \(\xrightarrow{\operatorname{Parse}}\) \(\text{Graph in PARC}\!\)
\(\operatorname{Conc}^0\) \(\xrightarrow{\operatorname{Parse}}\) \(\operatorname{Node}^0\)
\(\operatorname{Conc}_{j=1}^k s_j\) \(\xrightarrow{\operatorname{Parse}}\) \(\operatorname{Node}_{j=1}^k \operatorname{Parse} (s_j)\)
\(\operatorname{Surc}^0\) \(\xrightarrow{\operatorname{Parse}}\) \(\operatorname{Lobe}^0\)
\(\operatorname{Surc}_{j=1}^k s_j\) \(\xrightarrow{\operatorname{Parse}}\) \(\operatorname{Lobe}_{j=1}^k \operatorname{Parse} (s_j)\)


Table 14.1 Semantic Translation : Functional Form
\(\operatorname{Sentence}\) \(\xrightarrow[\operatorname{~~~~~~~~~~}]{\operatorname{Parse}}\) \(\operatorname{Graph}\) \(\xrightarrow[\operatorname{~~~~~~~~~~}]{\operatorname{Denotation}}\) \(\operatorname{Proposition}\)
\(s_j\!\) \(\xrightarrow{\operatorname{~~~~~~~~~~}}\) \(C_j\!\) \(\xrightarrow{\operatorname{~~~~~~~~~~}}\) \(q_j\!\)
\(\operatorname{Conc}^0\) \(\xrightarrow{\operatorname{~~~~~~~~~~}}\) \(\operatorname{Node}^0\) \(\xrightarrow{\operatorname{~~~~~~~~~~}}\) \(\underline{1}\)
\(\operatorname{Conc}^k_j s_j\) \(\xrightarrow{\operatorname{~~~~~~~~~~}}\) \(\operatorname{Node}^k_j C_j\) \(\xrightarrow{\operatorname{~~~~~~~~~~}}\) \(\operatorname{Conj}^k_j q_j\)
\(\operatorname{Surc}^0\) \(\xrightarrow{\operatorname{~~~~~~~~~~}}\) \(\operatorname{Lobe}^0\) \(\xrightarrow{\operatorname{~~~~~~~~~~}}\) \(\underline{0}\)
\(\operatorname{Surc}^k_j s_j\) \(\xrightarrow{\operatorname{~~~~~~~~~~}}\) \(\operatorname{Lobe}^k_j C_j\) \(\xrightarrow{\operatorname{~~~~~~~~~~}}\) \(\operatorname{Surj}^k_j q_j\)


Table 14.2 Semantic Translation : Equational Form
\(\downharpoonleft \operatorname{Sentence} \downharpoonright\) \(\stackrel{\operatorname{Parse}}{=}\) \(\downharpoonleft \operatorname{Graph} \downharpoonright\) \(\stackrel{\operatorname{Denotation}}{=}\) \(\operatorname{Proposition}\)
\(\downharpoonleft s_j \downharpoonright\) \(=\!\) \(\downharpoonleft C_j \downharpoonright\) \(=\!\) \(q_j\!\)
\(\downharpoonleft \operatorname{Conc}^0 \downharpoonright\) \(=\!\) \(\downharpoonleft \operatorname{Node}^0 \downharpoonright\) \(=\!\) \(\underline{1}\)
\(\downharpoonleft \operatorname{Conc}^k_j s_j \downharpoonright\) \(=\!\) \(\downharpoonleft \operatorname{Node}^k_j C_j \downharpoonright\) \(=\!\) \(\operatorname{Conj}^k_j q_j\)
\(\downharpoonleft \operatorname{Surc}^0 \downharpoonright\) \(=\!\) \(\downharpoonleft \operatorname{Lobe}^0 \downharpoonright\) \(=\!\) \(\underline{0}\)
\(\downharpoonleft \operatorname{Surc}^k_j s_j \downharpoonright\) \(=\!\) \(\downharpoonleft \operatorname{Lobe}^k_j C_j \downharpoonright\) \(=\!\) \(\operatorname{Surj}^k_j q_j\)


Table Stuff


fi‹x, y›
u =
v =
1 1 0 0
1 0 1 0
= u
= v
fj‹u, v›
x =
y =
1 1 1 0
1 0 0 1
= f‹u, v›
= g‹u, v›


A
u =
v =
1 1 0 0
1 0 1 0
= u
= v
B
x =
y =
1 1 1 0
1 0 0 1
= f‹u, v›
= g‹u, v›


u =
v =
1 1 0 0
1 0 1 0
= u
= v
x =
y =
1 1 1 0
1 0 0 1
= f‹u, v›
= g‹u, v›


u =
v =
x =
y =
1 1 0 0
1 0 1 0
1 1 1 0
1 0 0 1
= u
= v
= f‹u, v›
= g‹u, v›


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