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| | ===Translation Rules=== | | ===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%"
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| − | |- style="height:40px"
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| − | | align="right" colspan="2" | <math>\text{Logical Translation Rule 0}\!</math>
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| − | |- style="height:40px"
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| − | | style="border-top:1px solid black" | <math>\text{If}\!</math>
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| − | | style="border-top:1px solid black" |
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| − | <math>s_j ~\text{is a sentence about things in the universe X}</math>
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| − | | style="border-top:1px solid black" |
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| − | |- style="height:40px"
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| − | | <math>\text{and}\!</math>
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| − | | <math>p_j ~\text{is a proposition about things in the universe X}</math>
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| − | |- style="height:40px"
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| − | | width="2%" |
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| − | | width="18%" | <math>\text{such that:}\!</math>
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| − | | width="60%" |
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| − | | width="18%" |
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| − | | width="2%" |
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| − | |- style="height:40px"
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| − | | <math>\text{L0a.}\!</math>
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| − | | <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>
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| − | | <math>\text{the following equations are true:}\!</math>
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| − | |- style="height:48px"
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| − | | style="border-top:1px solid black" | <math>\text{L0b.}\!</math>
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| − | | style="border-top:1px solid black" |
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| − | <math>
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| − | \downharpoonleft \operatorname{Conc}_j^J s_j \downharpoonright ~=~
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| − | \operatorname{Conj}_j^J \downharpoonleft s_j \downharpoonright ~=~
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| − | \operatorname{Conj}_j^J p_j
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| − | </math>
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| − | | style="border-top:1px solid black" |
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| − | | style="border-top:1px solid black" |
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| − | |- style="height:48px"
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| − | | <math>\text{L0c.}\!</math>
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| − | <math>
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| − | \downharpoonleft \operatorname{Surc}_j^J s_j \downharpoonright ~=~
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| − | \operatorname{Surj}_j^J \downharpoonleft s_j \downharpoonright ~=~
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| − | \operatorname{Surj}_j^J p_j
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| − | </math>
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| − | |}
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| | <br> | | <br> |