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| | <math>\text{R4e.}\!</math> | | | <math>\text{R4e.}\!</math> |
| | <math>\upharpoonleft Q \upharpoonright (x) = \underline{1}</math> | | | <math>\upharpoonleft Q \upharpoonright (x) = \underline{1}</math> |
| + | | |
| + | |} |
| + | |
| + | <br> |
| + | |
| + | ===Translation Rules=== |
| + | |
| + | <br> |
| + | |
| + | {| 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%" |
| + | |- style="height:40px" |
| + | | |
| + | | |
| + | | align="right" colspan="2" | <math>\text{Logical Translation Rule 0}\!</math> |
| + | | |
| + | |- style="height:40px" |
| + | | style="border-top:1px solid black" | |
| + | | style="border-top:1px solid black" | <math>\text{If}\!</math> |
| + | | style="border-top:1px solid black" | |
| + | <math>s_j ~\text{is a sentence about things in the universe X}</math> |
| + | | style="border-top:1px solid black" | |
| + | | style="border-top:1px solid black" | |
| + | |- style="height:40px" |
| + | | |
| + | | <math>\text{and}\!</math> |
| + | | <math>p_j ~\text{is a proposition about things in the universe X}</math> |
| + | | |
| + | | |
| + | |- style="height:40px" |
| + | | width="2%" | |
| + | | width="18%" | <math>\text{such that:}\!</math> |
| + | | width="60%" | |
| + | | width="18%" | |
| + | | width="2%" | |
| + | |- style="height:40px" |
| + | | |
| + | | <math>\text{L0a.}\!</math> |
| + | | <math>\downharpoonleft s_j \downharpoonright ~=~ p_j, ~\text{for all}~ j \in J,</math> |
| + | | |
| + | | |
| + | |- style="height:40px" |
| + | | |
| + | | <math>\text{then}\!</math> |
| + | | <math>\text{the following equations are true:}\!</math> |
| + | | |
| + | | |
| + | |- style="height:48px" |
| + | | style="border-top:1px solid black" | |
| + | | style="border-top:1px solid black" | <math>\text{L0b.}\!</math> |
| + | | style="border-top:1px solid black" | |
| + | <math> |
| + | \downharpoonleft \operatorname{Conc}_j^J s_j \downharpoonright ~=~ |
| + | \operatorname{Conj}_j^J \downharpoonleft s_j \downharpoonright ~=~ |
| + | \operatorname{Conj}_j^J p_j |
| + | </math> |
| + | | style="border-top:1px solid black" | |
| + | | style="border-top:1px solid black" | |
| + | |- style="height:48px" |
| + | | |
| + | | <math>\text{L0c.}\!</math> |
| + | | |
| + | <math> |
| + | \downharpoonleft \operatorname{Surc}_j^J s_j \downharpoonright ~=~ |
| + | \operatorname{Surj}_j^J \downharpoonleft s_j \downharpoonright ~=~ |
| + | \operatorname{Surj}_j^J p_j |
| + | </math> |
| + | | |
| | | | | |
| |} | | |} |