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| |+ <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> |
| |- | | |- |
| + | | |
| | <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> |
| |- | | |- |
| + | | |
| | <math>\texttt{(} a \texttt{)}</math> | | | <math>\texttt{(} a \texttt{)}</math> |
| | <math>\operatorname{not}~ a</math> | | | <math>\operatorname{not}~ a</math> |
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| \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> |
| |- | | |- |
| + | | |
| | <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> |
| |- | | |- |
| + | | |
| | <math>\texttt{(} a, b \texttt{)}</math> | | | <math>\texttt{(} a, b \texttt{)}</math> |
| | | | | |
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| \end{matrix}</math> | | \end{matrix}</math> |
| |- | | |- |
| + | | |
| | <math>\texttt{((} a, b \texttt{))}</math> | | | <math>\texttt{((} a, b \texttt{))}</math> |
| | | | | |
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| \end{matrix}</math> | | \end{matrix}</math> |
| |- | | |- |
| + | | |
| | <math>\texttt{(} a, b, c \texttt{)}</math> | | | <math>\texttt{(} a, b, c \texttt{)}</math> |
| | | | | |
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| \end{matrix}</math> | | \end{matrix}</math> |
| |- | | |- |
| + | | |
| | <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> |
| |- | | |- |
| + | | |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
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| \end{matrix}</math></p> | | \end{matrix}</math></p> |
| |- | | |- |
| + | | |
| | <math>\texttt{(} x, \texttt{(} a \texttt{),(} b \texttt{),(} c \texttt{))}</math> | | | <math>\texttt{(} x, \texttt{(} a \texttt{),(} b \texttt{),(} c \texttt{))}</math> |
| | | | | |