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| | ===Logical Translation Rule 1=== | | ===Logical Translation Rule 1=== |
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| − | {| 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" width="100%"
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| − | |- style="height:48px; text-align:right"
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| − | | width="98%" | <math>\text{Logical Translation Rule 1}\!</math>
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| − | | width=2%" |
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| − | |}
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| − | {| align="center" cellpadding="0" cellspacing="0" width="100%"
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| − | |- style="height:48px"
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| − | | width="2%" style="border-top:1px solid black" |
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| − | | width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
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| − | | width="80%" style="border-top:1px solid black" |
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| − | <math>s ~\text{is a sentence about things in the universe X}</math>
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| − | |- style="height:48px"
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| − | | <math>\text{and}\!</math>
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| − | | <math>p ~\text{is a proposition} ~:~ X \to \underline\mathbb{B}</math>
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| − | |- style="height:48px"
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| − | | <math>\text{such that:}\!</math>
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| − | |- style="height:48px"
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| − | | <math>\text{L1a.}\!</math>
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| − | | <math>\downharpoonleft s \downharpoonright ~=~ p</math>
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| − | | <math>\text{then}\!</math>
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| − | | <math>\text{the following equations hold:}\!</math>
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| − | |}
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| − | {| align="center" cellpadding="0" cellspacing="0" style="text-align:center" width="100%"
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| − | |- style="height:56px"
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| − | | width="2%" style="border-top:1px solid black" |
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| − | | width="18%" style="border-top:1px solid black" align="left" | <math>\text{L1b}_{00}.\!</math>
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| − | | width="20%" style="border-top:1px solid black" |
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| − | <math>\downharpoonleft \operatorname{false} \downharpoonright</math>
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| − | | width="5%" style="border-top:1px solid black" | <math>=\!</math>
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| − | | width="20%" style="border-top:1px solid black" | <math>(~)</math>
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| − | | width="5%" style="border-top:1px solid black" | <math>=\!</math>
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| − | | width="30%" style="border-top:1px solid black" |
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| − | <math>\underline{0} ~:~ X \to \underline\mathbb{B}</math>
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| − | |- style="height:56px"
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| − | | align="left" | <math>\text{L1b}_{01}.\!</math>
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| − | | <math>\downharpoonleft \operatorname{not}~ s \downharpoonright</math>
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| − | | <math>=\!</math>
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| − | | <math>(\downharpoonleft s \downharpoonright)</math>
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| − | | <math>=\!</math>
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| − | | <math>(p) ~:~ X \to \underline\mathbb{B}</math>
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| − | |- style="height:56px"
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| − | | align="left" | <math>\text{L1b}_{10}.\!</math>
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| − | | <math>\downharpoonleft s \downharpoonright</math>
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| − | | <math>=\!</math>
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| − | | <math>\downharpoonleft s \downharpoonright</math>
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| − | | <math>=\!</math>
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| − | | <math>p ~:~ X \to \underline\mathbb{B}</math>
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| − | |- style="height:56px"
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| − | | align="left" | <math>\text{L1b}_{11}.\!</math>
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| − | | <math>\downharpoonleft \operatorname{true} \downharpoonright</math>
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| − | | <math>=\!</math>
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| − | | <math>((~))</math>
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| − | | <math>=\!</math>
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| − | | <math>\underline{1} ~:~ X \to \underline\mathbb{B}</math>
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| − | |}
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| − | |}
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| | <br> | | <br> |