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Revision as of 23:04, 27 January 2009
, 23:04, 27 January 2009→Syntactic Transformations: mathematical markup
A condition is ''amenable'' to a rule if any of its conceivable expressions formally match any of the expressions that are enumerated by the rule. Further, it requires the relegation of the other expressions to the production of a result. Thus, there is the choice of an initial expression that needs to be checked on input for whether it fits the antecedent condition and there are several types of output that are generated as a consequence, only a few of which are usually needed at any given time.
A condition is ''amenable'' to a rule if any of its conceivable expressions formally match any of the expressions that are enumerated by the rule. Further, it requires the relegation of the other expressions to the production of a result. Thus, there is the choice of an initial expression that needs to be checked on input for whether it fits the antecedent condition and there are several types of output that are generated as a consequence, only a few of which are usually needed at any given time.
<pre>
<br>
If S is a sentence
{| 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%"
|
{| align="center" cellpadding="0" cellspacing="0" width="100%"
and P is a proposition : U -> B, such that:
|- style="height:48px; text-align:right"
| width="98%" | <math>\text{Logical Translation Rule 1}\!</math>
L1a. [S] = P,
| width=2%" |
|}
then the following equations hold:
|-
|
{| 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>
| width="80%" style="border-top:1px solid black" |
<math>s ~\text{is a sentence about things in the universe X}</math>
|- style="height:48px"
</pre>
|
| <math>\text{and}\!</math>
| <math>p ~\text{is a proposition} ~:~ X \to \underline\mathbb{B}</math>
|- style="height:48px"
|
| <math>\text{such that:}\!</math>
|
|- style="height:48px"
|
| <math>\text{L1a.}\!</math>
| <math>\downharpoonleft s \downharpoonright ~=~ p</math>
|- style="height:48px"
|
| <math>\text{then}\!</math>
| <math>\text{the following equations hold:}\!</math>
|}
|-
|
{| align="center" cellpadding="0" cellspacing="0" style="text-align:center" width="100%"
|- style="height:52px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" align="left" | <math>\text{L1b}_{00}.\!</math>
| width="20%" style="border-top:1px solid black" |
<math>\downharpoonleft \operatorname{false} \downharpoonright</math>
| width="5%" style="border-top:1px solid black" | <math>=\!</math>
| width="20%" style="border-top:1px solid black" | <math>(~)</math>
| width="5%" style="border-top:1px solid black" | <math>=\!</math>
| width="30%" style="border-top:1px solid black" |
<math>\underline{0} ~:~ X \to \underline\mathbb{B}</math>
|- style="height:52px"
|
| align="left" | <math>\text{L1b}_{01}.\!</math>
| <math>\downharpoonleft \operatorname{not}~ s \downharpoonright</math>
| <math>=\!</math>
| <math>(\downharpoonleft s \downharpoonright)</math>
| <math>=\!</math>
| <math>(p) ~:~ X \to \underline\mathbb{B}</math>
|- style="height:52px"
|
| align="left" | <math>\text{L1b}_{10}.\!</math>
| <math>\downharpoonleft s \downharpoonright</math>
| <math>=\!</math>
| <math>\downharpoonleft s \downharpoonright</math>
| <math>=\!</math>
| <math>p ~:~ X \to \underline\mathbb{B}</math>
|- style="height:52px"
|
| align="left" | <math>\text{L1b}_{11}.\!</math>
| <math>\downharpoonleft \operatorname{true} \downharpoonright</math>
| <math>=\!</math>
| <math>((~))</math>
| <math>=\!</math>
| <math>\underline{1} ~:~ X \to \underline\mathbb{B}</math>
|}
|}
<br>
<br>
