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\operatorname{pie}~ a ~\operatorname{of~slices}~ b, c.
\operatorname{pie}~ a ~\operatorname{of~slices}~ b, c.
\end{matrix}</math>
\end{matrix}</math>
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===Work Area===
{| align="center" border="1" cellpadding="6" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"
|+ <math>\text{Table C.}~~\text{Dualing Interpretations}</math>
|- style="background:#f0f0ff"
| <math>\text{Graph}\!</math>
| <math>\text{String}\!</math>
| <math>\text{Existential}\!</math>
| <math>\text{Entitative}\!</math>
|-
|
<pre>
o-------------------o
| |
| @ |
| |
o-------------------o
</pre>
| <math>{}^{\backprime\backprime}\texttt{~}{}^{\prime\prime}</math>
| <math>\operatorname{true}.</math>
| <math>\operatorname{false}.</math>
|-
|
<pre>
o-------------------o
| |
| o |
| | |
| @ |
| |
o-------------------o
</pre>
| <math>\texttt{(~)}</math>
| <math>\operatorname{false}.</math>
| <math>\operatorname{true}.</math>
|-
|
<pre>
o-------------------o
| |
| a |
| @ |
| |
o-------------------o
</pre>
| <math>a\!</math>
| <math>a.\!</math>
| <math>a.\!</math>
|-
|
<pre>
o-------------------o
| |
| a |
| o |
| | |
| @ |
| |
o-------------------o
</pre>
| <math>\texttt{(} a \texttt{)}</math>
| <math>\lnot a</math>
| <math>\lnot a</math>
|-
|
<pre>
o-------------------o
| |
| a b c |
| @ |
| |
o-------------------o
</pre>
| <math>a~b~c</math>
| <math>a \land b \land c</math>
| <math>a \lor b \lor c</math>
|-
|
<pre>
o-------------------o
| |
| a b c |
| o o o |
| \|/ |
| o |
| | |
| @ |
| |
o-------------------o
</pre>
| <math>\texttt{((} a \texttt{)(} b \texttt{)(} c \texttt{))}</math>
| <math>a \lor b \lor c</math>
| <math>a \land b \land c</math>
|-
|
<pre>
o-------------------o
| |
| a b |
| o---o |
| | |
| @ |
| |
o-------------------o
</pre>
| <math>\texttt{(} a \texttt{(} b \texttt{))}</math>
| <math>a \Rightarrow b</math>
|
|-
|
<pre>
o-------------------o
| |
| a b |
| o---o |
| \ / |
| @ |
| |
o-------------------o
</pre>
| <math>\texttt{(} a, b \texttt{)}</math>
| <math>a \neq b</math>
| <math>a = b\!</math>
|-
|
<pre>
o-------------------o
| |
| a b |
| o---o |
| \ / |
| o |
| | |
| @ |
| |
o-------------------o
</pre>
| <math>\texttt{((} a, b \texttt{))}</math>
| <math>a = b\!</math>
| <math>a \neq b\!</math>
|-
|
<pre>
o-------------------o
| |
| a b c |
| o--o--o |
| \ / |
| \ / |
| @ |
| |
o-------------------o
</pre>
| <math>\texttt{(} a, b, c \texttt{)}</math>
|
<math>\begin{matrix}
\operatorname{just~one~of}
\\
a, b, c
\\
\operatorname{is~false}.
\end{matrix}</math>
|
<math>\begin{matrix}
\operatorname{not~just~one~of}
\\
a, b, c
\\
\operatorname{is~true}.
\end{matrix}</math>
|-
|
<pre>
o-------------------o
| |
| a b c |
| o o o |
| | | | |
| o--o--o |
| \ / |
| \ / |
| @ |
| |
o-------------------o
</pre>
| <math>\texttt{((} a \texttt{)}, \texttt{(} b \texttt{)}, \texttt{(} c \texttt{))}</math>
|
<math>\begin{matrix}
\operatorname{just~one~of}
\\
a, b, c
\\
\operatorname{is~true}.
\end{matrix}</math>
|
<math>\begin{matrix}
\operatorname{not~just~one~of}
\\
a, b, c
\\
\operatorname{is~false}.
\end{matrix}</math>
|-
|
<pre>
o-------------------o
| |
| b c |
| o o |
| a | | |
| o--o--o |
| \ / |
| \ / |
| @ |
| |
o-------------------o
</pre>
| <math>\texttt{(} a, \texttt{(} b \texttt{)}, \texttt{(} c \texttt{))}</math>
|
<math>\begin{matrix}
\operatorname{genus}~ a ~\operatorname{of~species}~ b, c.
\\[6pt]
\operatorname{partition}~ a ~\operatorname{into}~ b, c.
\\[6pt]
\operatorname{pie}~ a ~\operatorname{of~slices}~ b, c.
\end{matrix}</math>
|
|}
{| align="center" cellpadding="6" width="90%"
| align="center" |
<pre>
o-----------------o-----------------o-----------------o-----------------o
| Graph | String | Entitative | Existential |
o-----------------o-----------------o-----------------o-----------------o
| | | | |
| @ | " " | untrue. | true. |
o-----------------o-----------------o-----------------o-----------------o
| | | | |
| o | | | |
| | | | | |
| @ | ( ) | true. | untrue. |
o-----------------o-----------------o-----------------o-----------------o
| | | | |
| r | | | |
| @ | r | r. | r. |
o-----------------o-----------------o-----------------o-----------------o
| | | | |
| r | | | |
| o | | | |
| | | | | |
| @ | (r) | not r. | not r. |
o-----------------o-----------------o-----------------o-----------------o
| | | | |
| r s t | | | |
| @ | r s t | r or s or t. | r and s and t. |
o-----------------o-----------------o-----------------o-----------------o
| | | | |
| r s t | | | |
| o o o | | | |
| \|/ | | | |
| o | | | |
| | | | | |
| @ | ((r)(s)(t)) | r and s and t. | r or s or t. |
o-----------------o-----------------o-----------------o-----------------o
| | | | r implies s. |
| | | | |
| o r | | | if r then s. |
| | | | | |
| @ s | (r) s | not r, or s | no r sans s. |
o-----------------o-----------------o-----------------o-----------------o
| | | | r implies s. |
| r s | | | |
| o---o | | | if r then s. |
| | | | | |
| @ | (r (s)) | | no r sans s. |
o-----------------o-----------------o-----------------o-----------------o
| | | | |
| r s | | | |
| o---o | | |r exclusive-or s.|
| \ / | | | |
| @ | (r , s) | |r not equal to s.|
o-----------------o-----------------o-----------------o-----------------o
| | | | |
| r s | | | |
| o---o | | | |
| \ / | | | |
| o | | |r if & only if s.|
| | | | | |
| @ | ((r , s)) | |r equates with s.|
o-----------------o-----------------o-----------------o-----------------o
| | | | |
| r s t | | | |
| o--o--o | | | |
| \ / | | | |
| \ / | | | just one false |
| @ | (r , s , t) | | out of r, s, t. |
o-----------------o-----------------o-----------------o-----------------o
| | | | |
| r s t | | | |
| o o o | | | |
| | | | | | | |
| o--o--o | | | |
| \ / | | | |
| \ / | | | just one true |
| @ | ((r),(s),(t)) | | among r, s, t. |
o-----------------o-----------------o-----------------o-----------------o
| | | | genus t over |
| r s | | | species r, s. |
| o o | | | |
| t | | | | | partition t |
| o--o--o | | | among r & s. |
| \ / | | | |
| \ / | | | whole pie t: |
| @ | ( t ,(r),(s)) | | slices r, s. |
o-----------------o-----------------o-----------------o-----------------o
</pre>
|}
|}
