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Revision as of 20:28, 27 January 2009
, 20:28, 27 January 2009→Translation Rules
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{| align="center" cellpadding="2" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black" width="90%"
{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black" width="90%"
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{| align="center" cellpadding="0" cellspacing="0" style="text-align:right" width="100%"
|- style="height:48px"
| width="98%" | <math>\text{Logical Translation Rule 0}\!</math>
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| style="border-top:1px solid black" | <math>\text{If}\!</math>
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:48px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
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<math>s_j ~\text{is a sentence about things in the universe X}</math>
<math>s_j ~\text{is a sentence about things in the universe X}</math>
|- style="height:48px"
|- style="height:40px"
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| <math>\text{and}\!</math>
| <math>\text{and}\!</math>
| <math>p_j ~\text{is a proposition about things in the universe X}</math>
| <math>p_j ~\text{is a proposition about things in the universe X}</math>
|- style="height:48px"
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| <math>\text{such that:}\!</math>
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|- style="height:40px"
|- style="height:48px"
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| <math>\text{L0a.}\!</math>
| <math>\text{L0a.}\!</math>
| <math>\downharpoonleft s_j \downharpoonright ~=~ p_j, ~\text{for all}~ j \in J,</math>
| <math>\downharpoonleft s_j \downharpoonright ~=~ p_j, ~\text{for all}~ j \in J,</math>
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|- style="height:40px"
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| <math>\text{then}\!</math>
| <math>\text{then}\!</math>
| <math>\text{the following equations are true:}\!</math>
| <math>\text{the following equations are true:}\!</math>
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
| style="border-top:1px solid black" | <math>\text{L0b.}\!</math>
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| width="2%" style="border-top:1px solid black" |
<math>
| width="18%" style="border-top:1px solid black" | <math>\text{L0b.}\!</math>
\downharpoonleft \operatorname{Conc}_j^J s_j \downharpoonright ~=~
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\operatorname{Conj}_j^J \downharpoonleft s_j \downharpoonright ~=~
<math>\downharpoonleft \operatorname{Conc}_j^J s_j \downharpoonright</math>
| width="10%" style="border-top:1px solid black" | <math>=\!</math>
</math>
| width="20%" style="border-top:1px solid black" |
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<math>\operatorname{Conj}_j^J \downharpoonleft s_j \downharpoonright</math>
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| width="10%" style="border-top:1px solid black" | <math>=\!</math>
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| width="20%" style="border-top:1px solid black" |
<math>\operatorname{Conj}_j^J p_j</math>
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| <math>\text{L0c.}\!</math>
| <math>\text{L0c.}\!</math>
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| <math>\downharpoonleft \operatorname{Surc}_j^J s_j \downharpoonright</math>
<math>
| <math>=\!</math>
\downharpoonleft \operatorname{Surc}_j^J s_j \downharpoonright ~=~
| <math>\operatorname{Surj}_j^J \downharpoonleft s_j \downharpoonright</math>
\operatorname{Surj}_j^J \downharpoonleft s_j \downharpoonright ~=~
| <math>=\!</math>
\operatorname{Surj}_j^J p_j
| <math>\operatorname{Surj}_j^J p_j</math>
</math>
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