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Directory talk:Jon Awbrey/Papers/Differential Logic : Introduction (view source)
Revision as of 13:00, 30 June 2009
, 13:00, 30 June 2009→Logical Cacti: spacing + punctuation
</pre>
</pre>
| <math>{}^{\backprime\backprime}\texttt{~}{}^{\prime\prime}</math>
| <math>{}^{\backprime\backprime}\texttt{~}{}^{\prime\prime}</math>
| <math>\operatorname{true}</math>
| <math>\operatorname{true}.</math>
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</pre>
</pre>
| <math>\texttt{(~)}</math>
| <math>\texttt{(~)}</math>
| <math>\operatorname{false}</math>
| <math>\operatorname{false}.</math>
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</pre>
</pre>
| <math>a\!</math>
| <math>a\!</math>
| <math>a\!</math>
| <math>a.\!</math>
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</pre>
</pre>
| <math>\texttt{(} a \texttt{)}</math>
| <math>\texttt{(} a \texttt{)}</math>
| <math>\operatorname{not}~ a</math>
| <math>\operatorname{not}~ a.</math>
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</pre>
</pre>
| <math>a~b~c</math>
| <math>a~b~c</math>
| <math>a ~\operatorname{and}~ b ~\operatorname{and}~ c</math>
| <math>a ~\operatorname{and}~ b ~\operatorname{and}~ c.</math>
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</pre>
</pre>
| <math>\texttt{((} a \texttt{)(} b \texttt{)(} c \texttt{))}</math>
| <math>\texttt{((} a \texttt{)(} b \texttt{)(} c \texttt{))}</math>
| <math>a ~\operatorname{or}~ b ~\operatorname{or}~ c</math>
| <math>a ~\operatorname{or}~ b ~\operatorname{or}~ c.</math>
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<math>\begin{matrix}
<math>\begin{matrix}
a ~\operatorname{implies}~ b
a ~\operatorname{implies}~ b.
\\[4pt]
\\[6pt]
\operatorname{if}~ a ~\operatorname{then}~ b
\operatorname{if}~ a ~\operatorname{then}~ b.
\\[4pt]
\\[6pt]
\operatorname{no}~ a ~\operatorname{sans}~ b
\operatorname{not}~ a ~\operatorname{without}~ b.
\end{matrix}</math>
\end{matrix}</math>
|-
|-
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<math>\begin{matrix}
<math>\begin{matrix}
a ~\operatorname{exclusive~or}~ b
a ~\operatorname{exclusive-or}~ b.
\\[4pt]
\\[6pt]
a ~\operatorname{not~equal~to}~ b
a ~\operatorname{not~equal~to}~ b.
\end{matrix}</math>
\end{matrix}</math>
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|-
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<math>\begin{matrix}
<math>\begin{matrix}
a ~\operatorname{if~and~only~if}~ b
a ~\operatorname{if~and~only~if}~ b.
\\[4pt]
\\[6pt]
a ~\operatorname{equivalent~to}~ b
a ~\operatorname{equivalent~to}~ b.
\end{matrix}</math>
\end{matrix}</math>
|-
|-
a, b, c
a, b, c
\\
\\
\operatorname{is~false}
\operatorname{is~false}.
\end{matrix}</math>
\end{matrix}</math>
|-
|-
a, b, c
a, b, c
\\
\\
\operatorname{is~true}
\operatorname{is~true}.
\end{matrix}</math>
\end{matrix}</math>
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|-
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<math>\begin{matrix}
<math>\begin{matrix}
\operatorname{genus}~ a ~\operatorname{with~species}~ b, c
\operatorname{genus}~ a ~\operatorname{with~species}~ b, c.
\\[4pt]
\\[4pt]
\operatorname{partition}~ a ~\operatorname{among}~ b, c
\operatorname{partition}~ a ~\operatorname{among}~ b, c.
\\[4pt]
\\[4pt]
\operatorname{pie}~ a ~\operatorname{with~slices}~ b, c
\operatorname{pie}~ a ~\operatorname{with~slices}~ b, c.
\end{matrix}</math>
\end{matrix}</math>
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|}