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<pre>
<pre>
o-------------------o
o-------------------o
| |
| |
| a b |
| a b |
</pre>
</pre>
| <math>\texttt{((} a, b \texttt{))}</math>
| <math>\texttt{((} a, b \texttt{))}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
a = b
a = b
<pre>
<pre>
o-------------------o
o-------------------o
| |
| |
| b c |
| b c |
<br>
<br>
{| align="center" border="1" cellpadding="6" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"
|+ <math>\text{Table B.}~~\text{Entitative Interpretation}</math>
|- style="background:#f0f0ff"
| <math>\text{Cactus Graph}\!</math>
| <math>\text{Cactus Expression}\!</math>
| <math>\text{Interpretation}\!</math>
|-
|
<pre>
o-------------------o
| |
| @ |
| |
o-------------------o
</pre>
| <math>{}^{\backprime\backprime}\texttt{~}{}^{\prime\prime}</math>
| <math>\operatorname{false}.</math>
|-
|
<pre>
o-------------------o
| |
| o |
| | |
| @ |
| |
o-------------------o
</pre>
| <math>\texttt{(~)}</math>
| <math>\operatorname{true}.</math>
|-
|
<pre>
o-------------------o
| |
| a |
| @ |
| |
o-------------------o
</pre>
| <math>a\!</math>
| <math>a.\!</math>
|-
|
<pre>
o-------------------o
| |
| a |
| o |
| | |
| @ |
| |
o-------------------o
</pre>
| <math>\texttt{(} a \texttt{)}</math>
|
<math>\begin{matrix}
\tilde{a}
\\[6pt]
a^\prime
\\[6pt]
\lnot a
\\[6pt]
\operatorname{not}~ a.
\end{matrix}</math>
|-
|
<pre>
o-------------------o
| |
| a b c |
| @ |
| |
o-------------------o
</pre>
| <math>a~b~c</math>
|
<math>\begin{matrix}
a \lor b \lor c
\\[6pt]
a ~\operatorname{or}~ b ~\operatorname{or}~ c.
\end{matrix}</math>
|-
|
<pre>
o-------------------o
| |
| a b c |
| o o o |
| \|/ |
| o |
| | |
| @ |
| |
o-------------------o
</pre>
| <math>\texttt{((} a \texttt{)(} b \texttt{)(} c \texttt{))}</math>
|
<math>\begin{matrix}
a \land b \land c
\\[6pt]
a ~\operatorname{and}~ b ~\operatorname{and}~ c.
\end{matrix}</math>
|-
|
<pre>
o-------------------o
| |
| o a |
| | |
| @ b |
| |
o-------------------o
</pre>
| <math>\texttt{(} a \texttt{)} b</math>
|
<math>\begin{matrix}
a \Rightarrow b
\\[6pt]
a ~\operatorname{implies}~ b.
\\[6pt]
\operatorname{if}~ a ~\operatorname{then}~ b.
\\[6pt]
\operatorname{not}~ a, ~\operatorname{or}~ b.
\end{matrix}</math>
|-
|
<pre>
o-------------------o
| |
| a b |
| o---o |
| \ / |
| @ |
| |
o-------------------o
</pre>
| <math>\texttt{(} a, b \texttt{)}</math>
|
<math>\begin{matrix}
a = b
\\[6pt]
a \iff b
\\[6pt]
a ~\operatorname{equals}~ b.
\\[6pt]
a ~\operatorname{if~and~only~if}~ b.
\end{matrix}</math>
|-
|
<pre>
o-------------------o
| |
| a b |
| o---o |
| \ / |
| o |
| | |
| @ |
| |
o-------------------o
</pre>
| <math>\texttt{((} a, b \texttt{))}</math>
|
<math>\begin{matrix}
a + b
\\[6pt]
a \neq b
\\[6pt]
a ~\operatorname{exclusive-or}~ b.
\\[6pt]
a ~\operatorname{not~equal~to}~ b.
\end{matrix}</math>
|-
|
<pre>
o-------------------o
| |
| a b c |
| o--o--o |
| \ / |
| \ / |
| @ |
| |
o-------------------o
</pre>
| <math>\texttt{(} a, b, c \texttt{)}</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
</pre>
| <math>\texttt{((} a, b, c \texttt{))}</math>
|
<math>\begin{matrix}
\operatorname{just~one~of}
\\
a, b, c
\\
\operatorname{is~true}.
\end{matrix}</math>
|-
|
<pre>
o-------------------o
| |
| a |
| o |
| | b c |
| o--o--o |
| \ / |
| \ / |
| o |
| | |
| @ |
| |
o-------------------o
</pre>
| <math>\texttt{(((} a \texttt{)}, b, 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>
|}
==Differential Logic==
==Differential Logic==
