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

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<table align="center" cellpadding="4" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:90%">
  
 
<caption><font size="+2"><math>\text{Table 8.} ~~ \text{Simple Qualifiers of Propositions (Version 1)}</math></font></caption>
 
<caption><font size="+2"><math>\text{Table 8.} ~~ \text{Simple Qualifiers of Propositions (Version 1)}</math></font></caption>
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<math>f</math></td>
 
<math>f</math></td>
 
<td width="10%" style="border-bottom:1px solid black">
 
<td width="10%" style="border-bottom:1px solid black">
−
<math>\texttt{(} \ell_{11} \texttt{)}</math><br>
+
<math>\begin{matrix}
−
<math>No ~ u</math><br>
+
\texttt{(} \ell_{11} \texttt{)}
−
<math>is ~ v</math></td>
+
\\
 +
\mathrm{No} ~ u
 +
\\
 +
\mathrm{is} ~ v
 +
\end{matrix}</math></td>
 
<td width="10%" style="border-bottom:1px solid black">
 
<td width="10%" style="border-bottom:1px solid black">
−
<math>\texttt{(} \ell_{10} \texttt{)}</math><br>
+
<math>\begin{matrix}
−
<math>No ~ u</math><br>
+
\texttt{(} \ell_{10} \texttt{)}
−
<math>is ~ \texttt{(} v \texttt{)}</math></td>
+
\\
 +
\mathrm{No} ~ u
 +
\\
 +
\mathrm{is} ~ \texttt{(} v \texttt{)}
 +
\end{matrix}</math></td>
 
<td width="10%" style="border-bottom:1px solid black">
 
<td width="10%" style="border-bottom:1px solid black">
−
<math>\texttt{(} \ell_{01} \texttt{)}</math><br>
+
<math>\begin{matrix}
−
<math>No ~ \texttt{(} u \texttt{)}</math><br>
+
\texttt{(} \ell_{01} \texttt{)}
−
<math>is ~ v</math></td>
+
\\
 +
\mathrm{No} ~ \texttt{(} u \texttt{)}
 +
\\
 +
\mathrm{is} ~ v
 +
\end{matrix}</math></td>
 
<td width="10%" style="border-bottom:1px solid black">
 
<td width="10%" style="border-bottom:1px solid black">
−
<math>\texttt{(} \ell_{00} \texttt{)}</math><br>
+
<math>\begin{matrix}
−
<math>No ~ \texttt{(} u \texttt{)}</math><br>
+
\texttt{(} \ell_{00} \texttt{)}
−
<math>is ~ \texttt{(} v \texttt{)}</math></td>
+
\\
 +
\mathrm{No} ~ \texttt{(} u \texttt{)}
 +
\\
 +
\mathrm{is} ~ \texttt{(} v \texttt{)}
 +
\end{matrix}</math></td>
 
<td width="10%" style="border-bottom:1px solid black">
 
<td width="10%" style="border-bottom:1px solid black">
−
<math>\ell_{00}</math><br>
+
<math>\begin{matrix}
−
<math>Some ~ \texttt{(} u \texttt{)}</math><br>
+
\ell_{00}
−
<math>is   ~ \texttt{(} v \texttt{)}</math></td>
+
\\
 +
\mathrm{Some} ~ \texttt{(} u \texttt{)}
 +
\\
 +
\mathrm{is} ~ \texttt{(} v \texttt{)}
 +
\end{matrix}</math></td>
 
<td width="10%" style="border-bottom:1px solid black">
 
<td width="10%" style="border-bottom:1px solid black">
−
<math>\ell_{01}</math><br>
+
<math>\begin{matrix}
−
<math>Some ~ \texttt{(} u \texttt{)}</math><br>
+
\ell_{01}
−
<math>is   ~ v</math></td>
+
\\
 +
\mathrm{Some} ~ \texttt{(} u \texttt{)}
 +
\\
 +
\mathrm{is} ~ v
 +
\end{matrix}</math></td>
 
<td width="10%" style="border-bottom:1px solid black">
 
<td width="10%" style="border-bottom:1px solid black">
−
<math>\ell_{10}</math><br>
+
<math>\begin{matrix}
−
<math>Some ~ u</math><br>
+
\ell_{10}
−
<math>is   ~ \texttt{(} v \texttt{)}</math></td>
+
\\
 +
\mathrm{Some} ~ u
 +
\\
 +
\mathrm{is} ~ \texttt{(} v \texttt{)}
 +
\end{matrix}</math></td>
 
<td width="10%" style="border-bottom:1px solid black">
 
<td width="10%" style="border-bottom:1px solid black">
−
<math>\ell_{11}</math><br>
+
<math>\begin{matrix}
−
<math>Some ~ u</math><br>
+
\ell_{11}
−
<math>is   ~ v</math></td></tr>
+
\\
 +
\mathrm{Some} ~ u
 +
\\
 +
\mathrm{is} ~ v
 +
\end{matrix}</math></td></tr>
  
 
<tr>
 
<tr>
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<br>
 
<br>
  
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<table align="center" cellpadding="1" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:90%">
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<table align="center" cellpadding="4" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:90%">
  
 
<caption><font size="+2"><math>\text{Table 9.} ~~ \text{Simple Qualifiers of Propositions (Version 2)}</math></font></caption>
 
<caption><font size="+2"><math>\text{Table 9.} ~~ \text{Simple Qualifiers of Propositions (Version 2)}</math></font></caption>
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<math>f</math></td>
 
<math>f</math></td>
 
<td width="10%" style="border-bottom:1px solid black">
 
<td width="10%" style="border-bottom:1px solid black">
−
<math>\texttt{(} \ell_{11} \texttt{)}</math><br>
+
<math>\begin{matrix}
−
<math>No ~ u</math><br>
+
\texttt{(} \ell_{11} \texttt{)}
−
<math>is ~ v</math></td>
+
\\
 +
\mathrm{No} ~ u
 +
\\
 +
\mathrm{is} ~ v
 +
\end{matrix}</math></td>
 
<td width="10%" style="border-bottom:1px solid black">
 
<td width="10%" style="border-bottom:1px solid black">
−
<math>\texttt{(} \ell_{10} \texttt{)}</math><br>
+
<math>\begin{matrix}
−
<math>No ~ u</math><br>
+
\texttt{(} \ell_{10} \texttt{)}
−
<math>is ~ \texttt{(} v \texttt{)}</math></td>
+
\\
 +
\mathrm{No} ~ u
 +
\\
 +
\mathrm{is} ~ \texttt{(} v \texttt{)}
 +
\end{matrix}</math></td>
 
<td width="10%" style="border-bottom:1px solid black">
 
<td width="10%" style="border-bottom:1px solid black">
−
<math>\texttt{(} \ell_{01} \texttt{)}</math><br>
+
<math>\begin{matrix}
−
<math>No ~ \texttt{(} u \texttt{)}</math><br>
+
\texttt{(} \ell_{01} \texttt{)}
−
<math>is ~ v</math></td>
+
\\
 +
\mathrm{No} ~ \texttt{(} u \texttt{)}
 +
\\
 +
\mathrm{is} ~ v
 +
\end{matrix}</math></td>
 
<td width="10%" style="border-bottom:1px solid black">
 
<td width="10%" style="border-bottom:1px solid black">
−
<math>\texttt{(} \ell_{00} \texttt{)}</math><br>
+
<math>\begin{matrix}
−
<math>No ~ \texttt{(} u \texttt{)}</math><br>
+
\texttt{(} \ell_{00} \texttt{)}
−
<math>is ~ \texttt{(} v \texttt{)}</math></td>
+
\\
 +
\mathrm{No} ~ \texttt{(} u \texttt{)}
 +
\\
 +
\mathrm{is} ~ \texttt{(} v \texttt{)}
 +
\end{matrix}</math></td>
 
<td width="10%" style="border-bottom:1px solid black">
 
<td width="10%" style="border-bottom:1px solid black">
−
<math>\ell_{00}</math><br>
+
<math>\begin{matrix}
−
<math>Some ~ \texttt{(} u \texttt{)}</math><br>
+
\ell_{00}
−
<math>is   ~ \texttt{(} v \texttt{)}</math></td>
+
\\
 +
\mathrm{Some} ~ \texttt{(} u \texttt{)}
 +
\\
 +
\mathrm{is} ~ \texttt{(} v \texttt{)}
 +
\end{matrix}</math></td>
 
<td width="10%" style="border-bottom:1px solid black">
 
<td width="10%" style="border-bottom:1px solid black">
−
<math>\ell_{01}</math><br>
+
<math>\begin{matrix}
−
<math>Some ~ \texttt{(} u \texttt{)}</math><br>
+
\ell_{01}
−
<math>is   ~ v</math></td>
+
\\
 +
\mathrm{Some} ~ \texttt{(} u \texttt{)}
 +
\\
 +
\mathrm{is} ~ v
 +
\end{matrix}</math></td>
 
<td width="10%" style="border-bottom:1px solid black">
 
<td width="10%" style="border-bottom:1px solid black">
−
<math>\ell_{10}</math><br>
+
<math>\begin{matrix}
−
<math>Some ~ u</math><br>
+
\ell_{10}
−
<math>is   ~ \texttt{(} v \texttt{)}</math></td>
+
\\
 +
\mathrm{Some} ~ u
 +
\\
 +
\mathrm{is} ~ \texttt{(} v \texttt{)}
 +
\end{matrix}</math></td>
 
<td width="10%" style="border-bottom:1px solid black">
 
<td width="10%" style="border-bottom:1px solid black">
−
<math>\ell_{11}</math><br>
+
<math>\begin{matrix}
−
<math>Some ~ u</math><br>
+
\ell_{11}
−
<math>is   ~ v</math></td></tr>
+
\\
 +
\mathrm{Some} ~ u
 +
\\
 +
\mathrm{is} ~ v
 +
\end{matrix}</math></td></tr>
  
 
<tr>
 
<tr>

Revision as of 02:58, 23 November 2009

The following Tables develop these ideas in more detail.


\(\text{Table 8.} ~~ \text{Simple Qualifiers of Propositions (Version 1)}\)
\(\begin{matrix}u\!:\\v\!:\end{matrix}\) \(\begin{matrix}1100\\1010\end{matrix}\) \(f\) \(\begin{matrix} \texttt{(} \ell_{11} \texttt{)} \\ \mathrm{No} ~ u \\ \mathrm{is} ~ v \end{matrix}\) \(\begin{matrix} \texttt{(} \ell_{10} \texttt{)} \\ \mathrm{No} ~ u \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{matrix}\) \(\begin{matrix} \texttt{(} \ell_{01} \texttt{)} \\ \mathrm{No} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ v \end{matrix}\) \(\begin{matrix} \texttt{(} \ell_{00} \texttt{)} \\ \mathrm{No} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{matrix}\) \(\begin{matrix} \ell_{00} \\ \mathrm{Some} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{matrix}\) \(\begin{matrix} \ell_{01} \\ \mathrm{Some} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ v \end{matrix}\) \(\begin{matrix} \ell_{10} \\ \mathrm{Some} ~ u \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{matrix}\) \(\begin{matrix} \ell_{11} \\ \mathrm{Some} ~ u \\ \mathrm{is} ~ v \end{matrix}\)
\(f_{0}\) \(0000\) \(\texttt{(~)}\) 1 1 1 1 0 0 0 0
\(f_{1}\) \(0001\) \(\texttt{(} u \texttt{)(} v \texttt{)}\) 1 1 1 0 1 0 0 0
\(f_{2}\) \(0010\) \(\texttt{(} u\texttt{)} ~ v\) 1 1 0 1 0 1 0 0
\(f_{3}\) \(0011\) \(\texttt{(} u \texttt{)}\) 1 1 0 0 1 1 0 0
\(f_{4}\) \(0100\) \(u ~ \texttt{(} v \texttt{)}\) 1 0 1 1 0 0 1 0
\(f_{5}\) \(0101\) \(\texttt{(} v \texttt{)}\) 1 0 1 0 1 0 1 0
\(f_{6}\) \(0110\) \(\texttt{(} u \texttt{,} v \texttt{)}\) 1 0 0 1 0 1 1 0
\(f_{7}\) \(0111\) \(\texttt{(} u ~ v \texttt{)}\) 1 0 0 0 1 1 1 0
\(f_{8}\) \(1000\) \(u ~ v\) 0 1 1 1 0 0 0 1
\(f_{9}\) \(1001\) \(\texttt{((} u \texttt{,} v \texttt{))}\) 0 1 1 0 1 0 0 1
\(f_{10}\) \(1010\) \(v\) 0 1 0 1 0 1 0 1
\(f_{11}\) \(1011\) \(\texttt{(} u ~ \texttt{(} v \texttt{))}\) 0 1 0 0 1 1 0 1
\(f_{12}\) \(1100\) \(u\) 0 0 1 1 0 0 1 1
\(f_{13}\) \(1101\) \(\texttt{((} u \texttt{)} ~ v \texttt{)}\) 0 0 1 0 1 0 1 1
\(f_{14}\) \(1110\) \(\texttt{((} u \texttt{)(} v \texttt{))}\) 0 0 0 1 0 1 1 1
\(f_{15}\) \(1111\) \(\texttt{((~))}\) 0 0 0 0 1 1 1 1


\(\text{Table 9.} ~~ \text{Simple Qualifiers of Propositions (Version 2)}\)
\(\begin{matrix}u\!:\\v\!:\end{matrix}\) \(\begin{matrix}1100\\1010\end{matrix}\) \(f\) \(\begin{matrix} \texttt{(} \ell_{11} \texttt{)} \\ \mathrm{No} ~ u \\ \mathrm{is} ~ v \end{matrix}\) \(\begin{matrix} \texttt{(} \ell_{10} \texttt{)} \\ \mathrm{No} ~ u \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{matrix}\) \(\begin{matrix} \texttt{(} \ell_{01} \texttt{)} \\ \mathrm{No} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ v \end{matrix}\) \(\begin{matrix} \texttt{(} \ell_{00} \texttt{)} \\ \mathrm{No} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{matrix}\) \(\begin{matrix} \ell_{00} \\ \mathrm{Some} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{matrix}\) \(\begin{matrix} \ell_{01} \\ \mathrm{Some} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ v \end{matrix}\) \(\begin{matrix} \ell_{10} \\ \mathrm{Some} ~ u \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{matrix}\) \(\begin{matrix} \ell_{11} \\ \mathrm{Some} ~ u \\ \mathrm{is} ~ v \end{matrix}\)
\(f_{0}\) \(0000\) \(\texttt{(~)}\) 1 1 1 1 0 0 0 0
\(f_{1}\) \(0001\) \(\texttt{(} u \texttt{)(} v \texttt{)}\) 1 1 1 0 1 0 0 0
\(f_{2}\) \(0010\) \(\texttt{(} u\texttt{)} ~ v\) 1 1 0 1 0 1 0 0
\(f_{4}\) \(0100\) \(u ~ \texttt{(} v \texttt{)}\) 1 0 1 1 0 0 1 0
\(f_{8}\) \(1000\) \(u ~ v\) 0 1 1 1 0 0 0 1
\(f_{3}\) \(0011\) \(\texttt{(} u \texttt{)}\) 1 1 0 0 1 1 0 0
\(f_{12}\) \(1100\) \(u\) 0 0 1 1 0 0 1 1
\(f_{6}\) \(0110\) \(\texttt{(} u \texttt{,} v \texttt{)}\) 1 0 0 1 0 1 1 0
\(f_{9}\) \(1001\) \(\texttt{((} u \texttt{,} v \texttt{))}\) 0 1 1 0 1 0 0 1
\(f_{5}\) \(0101\) \(\texttt{(} v \texttt{)}\) 1 0 1 0 1 0 1 0
\(f_{10}\) \(1010\) \(v\) 0 1 0 1 0 1 0 1
\(f_{7}\) \(0111\) \(\texttt{(} u ~ v \texttt{)}\) 1 0 0 0 1 1 1 0
\(f_{11}\) \(1011\) \(\texttt{(} u ~ \texttt{(} v \texttt{))}\) 0 1 0 0 1 1 0 1
\(f_{13}\) \(1101\) \(\texttt{((} u \texttt{)} ~ v \texttt{)}\) 0 0 1 0 1 0 1 1
\(f_{14}\) \(1110\) \(\texttt{((} u \texttt{)(} v \texttt{))}\) 0 0 0 1 0 1 1 1
\(f_{15}\) \(1111\) \(\texttt{((~))}\) 0 0 0 0 1 1 1 1


\(\text{Table 10.} ~~ \text{Relation of Quantifiers to Higher Order Propositions}\)
\(\mathrm{Mnemonic}\) \(\mathrm{Category}\) \(\mathrm{Classical~Form}\) \(\mathrm{Alternate~Form}\) \(\mathrm{Symmetric~Form}\) \(\mathrm{Operator}\)
\(\mathrm{E}\)
\(\mathrm{Exclusive}\)		 \(\mathrm{Universal}\)
\(\mathrm{Negative}\)		 \(\mathrm{All} ~ u ~ \mathrm{is} ~ \texttt{(} v \texttt{)}\)   \(\mathrm{No} ~ u ~ \mathrm{is} ~ v\) \(\texttt{(} \ell_{11} \texttt{)}\)
\(\mathrm{A}\)
\(\mathrm{Absolute}\)		 \(\mathrm{Universal}\)
\(\mathrm{Affirmative}\)		 \(\mathrm{All} ~ u ~ \mathrm{is} ~ v\)   \(\mathrm{No} ~ u ~ \mathrm{is} ~ \texttt{(} v \texttt{)}\) \(\texttt{(} \ell_{10} \texttt{)}\)
    \(\mathrm{All} ~ v ~ \mathrm{is} ~ u\) \(\mathrm{No} ~ v ~ \mathrm{is} ~ \texttt{(} u \texttt{)}\) \(\mathrm{No} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ v\) \(\texttt{(} \ell_{01} \texttt{)}\)
    \(\mathrm{All} ~ \texttt{(} v \texttt{)} ~ \mathrm{is} ~ u\) \(\mathrm{No} ~ \texttt{(} v \texttt{)} ~ \mathrm{is} ~ \texttt{(} u \texttt{)}\) \(\mathrm{No} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ \texttt{(} v \texttt{)}\) \(\texttt{(} \ell_{00} \texttt{)}\)
    \(\mathrm{Some} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ \texttt{(} v \texttt{)}\)   \(\mathrm{Some} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ \texttt{(} v \texttt{)}\) \(\ell_{00}\)
    \(\mathrm{Some} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ v\)   \(\mathrm{Some} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ v\) \(\ell_{01}\)
\(\mathrm{O}\)
\(\mathrm{Obtrusive}\)		 \(\mathrm{Particular}\)
\(\mathrm{Negative}\)		 \(\mathrm{Some} ~ u ~ \mathrm{is} ~ \texttt{(} v \texttt{)}\)   \(\mathrm{Some} ~ u ~ \mathrm{is} ~ \texttt{(} v \texttt{)}\) \(\ell_{10}\)
\(\mathrm{I}\)
\(\mathrm{Indefinite}\)		 \(\mathrm{Particular}\)
\(\mathrm{Affirmative}\)		 \(\mathrm{Some} ~ u ~ \mathrm{is} ~ v\)   \(\mathrm{Some} ~ u ~ \mathrm{is} ~ v\) \(\ell_{11}\)


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