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

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<td><math>\mathrm{E}</math><br><math>\mathrm{Exclusive}</math></td>
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<td><math>\mathrm{Universal}</math><br><math>\mathrm{Negative}</math></td>
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\mathrm{E}
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\\
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\mathrm{Exclusive}
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\end{matrix}</math></td>
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<td><math>\begin{matrix}
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\mathrm{Universal}
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\mathrm{Negative}
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\end{matrix}</math></td>
 
<td><math>\mathrm{All} ~ u ~ \mathrm{is} ~ \texttt{(} v \texttt{)}</math></td>
 
<td><math>\mathrm{All} ~ u ~ \mathrm{is} ~ \texttt{(} v \texttt{)}</math></td>
 
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<td style="border-bottom:1px solid black"><math>\mathrm{A}</math><br><math>\mathrm{Absolute}</math></td>
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<td style="border-bottom:1px solid black"><math>\mathrm{Universal}</math><br><math>\mathrm{Affirmative}</math></td>
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<math>\begin{matrix}
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\mathrm{A}
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\mathrm{Absolute}
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\mathrm{Universal}
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\mathrm{Affirmative}
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\end{matrix}</math></td>
 
<td style="border-bottom:1px solid black"><math>\mathrm{All} ~ u ~ \mathrm{is} ~ v</math></td>
 
<td style="border-bottom:1px solid black"><math>\mathrm{All} ~ u ~ \mathrm{is} ~ v</math></td>
 
<td style="border-bottom:1px solid black">&nbsp;</td>
 
<td style="border-bottom:1px solid black">&nbsp;</td>

Revision as of 21:02, 23 November 2009

Wet Paint


\(\text{Table 8.} ~~ \text{Simple Qualifiers of Propositions (Version 1)}\)
\(\begin{matrix}u\!:\\v\!:\end{matrix}\) \(\begin{matrix}1100\\1010\end{matrix}\) \(f\) \(\begin{smallmatrix} \texttt{(} \ell_{11} \texttt{)} \\ \mathrm{No} ~ u \\ \mathrm{is} ~ v \end{smallmatrix}\) \(\begin{smallmatrix} \texttt{(} \ell_{10} \texttt{)} \\ \mathrm{No} ~ u \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{smallmatrix}\) \(\begin{smallmatrix} \texttt{(} \ell_{01} \texttt{)} \\ \mathrm{No} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ v \end{smallmatrix}\) \(\begin{smallmatrix} \texttt{(} \ell_{00} \texttt{)} \\ \mathrm{No} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{smallmatrix}\) \(\begin{smallmatrix} \ell_{00} \\ \mathrm{Some} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{smallmatrix}\) \(\begin{smallmatrix} \ell_{01} \\ \mathrm{Some} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ v \end{smallmatrix}\) \(\begin{smallmatrix} \ell_{10} \\ \mathrm{Some} ~ u \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{smallmatrix}\) \(\begin{smallmatrix} \ell_{11} \\ \mathrm{Some} ~ u \\ \mathrm{is} ~ v \end{smallmatrix}\)
\(f_{0}\) \(0000\) \(\texttt{(~)}\) 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


\(\text{Table 9.} ~~ \text{Simple Qualifiers of Propositions (Version 2)}\)
\(\begin{matrix}u\!:\\v\!:\end{matrix}\) \(\begin{matrix}1100\\1010\end{matrix}\) \(f\) \(\begin{smallmatrix} \texttt{(} \ell_{11} \texttt{)} \\ \mathrm{No} ~ u \\ \mathrm{is} ~ v \end{smallmatrix}\) \(\begin{smallmatrix} \texttt{(} \ell_{10} \texttt{)} \\ \mathrm{No} ~ u \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{smallmatrix}\) \(\begin{smallmatrix} \texttt{(} \ell_{01} \texttt{)} \\ \mathrm{No} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ v \end{smallmatrix}\) \(\begin{smallmatrix} \texttt{(} \ell_{00} \texttt{)} \\ \mathrm{No} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{smallmatrix}\) \(\begin{smallmatrix} \ell_{00} \\ \mathrm{Some} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{smallmatrix}\) \(\begin{smallmatrix} \ell_{01} \\ \mathrm{Some} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ v \end{smallmatrix}\) \(\begin{smallmatrix} \ell_{10} \\ \mathrm{Some} ~ u \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{smallmatrix}\) \(\begin{smallmatrix} \ell_{11} \\ \mathrm{Some} ~ u \\ \mathrm{is} ~ v \end{smallmatrix}\)
\(f_{0}\) \(0000\) \(\texttt{(~)}\) 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


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


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