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Directory talk:Jon Awbrey/Papers/Differential Logic : Introduction (view source)
Revision as of 15:35, 2 July 2009
, 15:35, 2 July 2009→Logical Cacti
|+ <math>\text{Table 1.}~~\text{Syntax and Semantics of a Calculus for Propositional Logic}</math>
|+ <math>\text{Table 1.}~~\text{Syntax and Semantics of a Calculus for Propositional Logic}</math>
|- style="background:#f0f0ff"
|- style="background:#f0f0ff"
| <math>\text{Graph}\!</math>
| <math>\text{Expression}\!</math>
| <math>\text{Expression}\!</math>
| <math>\text{Interpretation}\!</math>
| <math>\text{Interpretation}\!</math>
| <math>\text{Other Notations}\!</math>
| <math>\text{Other Notations}\!</math>
|-
|-
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| <math>~</math>
| <math>~</math>
| <math>\operatorname{true}</math>
| <math>\operatorname{true}</math>
| <math>1\!</math>
| <math>1\!</math>
|-
|-
|
| <math>\texttt{(~)}</math>
| <math>\texttt{(~)}</math>
| <math>\operatorname{false}</math>
| <math>\operatorname{false}</math>
| <math>0\!</math>
| <math>0\!</math>
|-
|-
|
| <math>a\!</math>
| <math>a\!</math>
| <math>a\!</math>
| <math>a\!</math>
| <math>a\!</math>
| <math>a\!</math>
|-
|-
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| <math>\texttt{(} a \texttt{)}</math>
| <math>\texttt{(} a \texttt{)}</math>
| <math>\operatorname{not}~ a</math>
| <math>\operatorname{not}~ a</math>
\end{matrix}</math>
\end{matrix}</math>
|-
|-
|
| <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>
| <math>a \land b \land c</math>
| <math>a \land b \land c</math>
|-
|-
|
| <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>
| <math>a \lor b \lor c</math>
| <math>a \lor b \lor c</math>
|-
|-
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| <math>\texttt{(} a \texttt{(} b \texttt{))}</math>
| <math>\texttt{(} a \texttt{(} b \texttt{))}</math>
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| <math>a \Rightarrow b</math>
| <math>a \Rightarrow b</math>
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|-
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| <math>\texttt{(} a, b \texttt{)}</math>
| <math>\texttt{(} a, b \texttt{)}</math>
|
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\end{matrix}</math>
\end{matrix}</math>
|-
|-
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| <math>\texttt{((} a, b \texttt{))}</math>
| <math>\texttt{((} a, b \texttt{))}</math>
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\end{matrix}</math>
\end{matrix}</math>
|-
|-
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| <math>\texttt{(} a, b, c \texttt{)}</math>
| <math>\texttt{(} a, b, c \texttt{)}</math>
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\end{matrix}</math>
\end{matrix}</math>
|-
|-
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| <math>\texttt{((} a \texttt{),(} b \texttt{),(} c \texttt{))}</math>
| <math>\texttt{((} a \texttt{),(} b \texttt{),(} c \texttt{))}</math>
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\end{matrix}</math>
\end{matrix}</math>
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|-
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<math>\begin{matrix}
<math>\begin{matrix}
\end{matrix}</math></p>
\end{matrix}</math></p>
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|-
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| <math>\texttt{(} x, \texttt{(} a \texttt{),(} b \texttt{),(} c \texttt{))}</math>
| <math>\texttt{(} x, \texttt{(} a \texttt{),(} b \texttt{),(} c \texttt{))}</math>
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