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Revision as of 03:11, 11 July 2008
, 03:11, 11 July 2008→Tables of Propositional Forms: HTML → TeX
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Propositional forms on two variables correspond to boolean functions ''f'' : '''B'''<sup>2</sup> → '''B'''. In Table 7 each function ''f''<sub>''i''</sub> is indexed by the values that it takes on the points of the universe ''X''<sup> •</sup> = [''x'', ''y''] <math>\cong</math> '''B'''<sup>2</sup>. Converting the binary index thus generated to a decimal equivalent, we obtain the functional nicknames that are listed in the first column. The 2<sup>2</sup> points of the universe ''X''<sup> •</sup> are coordinated as a space of type '''B'''<sup>2</sup>, as indicated under the heading of the Table, where the coordinate projections ''x'' and ''y'' run through the various combinations of their values in '''B'''.
Propositional forms on two variables correspond to boolean functions ''f'' : '''B'''<sup>2</sup> → '''B'''. In Table 7 each function ''f''<sub>''i''</sub> is indexed by the values that it takes on the points of the universe ''X''<sup> •</sup> = [''x'', ''y''] <math>\cong</math> '''B'''<sup>2</sup>. Converting the binary index thus generated to a decimal equivalent, we obtain the functional nicknames that are listed in the first column. The 2<sup>2</sup> points of the universe ''X''<sup> •</sup> are coordinated as a space of type '''B'''<sup>2</sup>, as indicated under the heading of the Table, where the coordinate projections ''x'' and ''y'' run through the various combinations of their values in '''B'''.
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:96%"
|+ '''Table 7. Propositional Forms on Two Variables'''
|+ '''Table 7. Propositional Forms on Two Variables'''
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<math>\begin{matrix}\mathcal{L}_1 \\ \mbox{Decimal}\end{matrix}</math>
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<math>\begin{matrix}\mathcal{L}_2 \\ \mbox{Binary}\end{matrix}</math>
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<math>\begin{matrix}\mathcal{L}_3 \\ \mbox{Vector}\end{matrix}</math>
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<math>\begin{matrix}\mathcal{L}_4 \\ \mbox{Cactus}\end{matrix}</math>
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<math>\begin{matrix}\mathcal{L}_5 \\ \mbox{English}\end{matrix}</math>
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<math>\begin{matrix}\mathcal{L}_6 \\ \mbox{Ordinary}\end{matrix}</math>
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| f<sub>0</sub> || f<sub>0000</sub> || 0 0 0 0 || ( ) || false || 0
| f<sub>0</sub> || f<sub>0000</sub> || 0 0 0 0 || ( ) || false || 0
