http://lem12.uksw.edu.pl/index.php?title=Axiomatic_definitions_of_sublanguages_of_Loglan%2782&feed=atom&action=history
Axiomatic definitions of sublanguages of Loglan'82 - Historia wersji
2024-03-29T05:18:15Z
Historia wersji tej strony wiki
MediaWiki 1.23.8
http://lem12.uksw.edu.pl/index.php?title=Axiomatic_definitions_of_sublanguages_of_Loglan%2782&diff=1547&oldid=prev
AndrzejSalwicki: /* Characters */
2014-11-27T14:21:18Z
<p><span dir="auto"><span class="autocomment">Characters</span></span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← poprzednia wersja</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Wersja z 14:21, 27 lis 2014</td>
</tr><tr><td colspan="2" class="diff-lineno">Linia 83:</td>
<td colspan="2" class="diff-lineno">Linia 83:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>I.e. ''the execution of three instructions causes swap of the values of variables'' <math> c_1, c_2 </math>.<br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>I.e. ''the execution of three instructions causes swap of the values of variables'' <math> c_1, c_2 </math>.<br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>'''Proof''' uses two axioms of algorithmic logic: <br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>'''Proof''' uses two axioms of algorithmic logic: <br /></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax:=}<del class="diffchange diffchange-inline">\fbox{</del>[x:=\tau]\alpha \Leftrightarrow \alpha(x/\tau)<del class="diffchange diffchange-inline">} </del>\end{equation} </math> <br /></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax:=}[x:=\tau]\alpha \Leftrightarrow \alpha(x/\tau) \end{equation} </math> <br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>this axiom of assignment instruction reads: ''formula '' <math>\alpha(x/\tau)</math> '' holds iff after execution of instruction  '' <math>x:=\tau</math> ''formula  ''<math>\alpha</math> '' holds.''<br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>this axiom of assignment instruction reads: ''formula '' <math>\alpha(x/\tau)</math> '' holds iff after execution of instruction  '' <math>x:=\tau</math> ''formula  ''<math>\alpha</math> '' holds.''<br /></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax ;}<del class="diffchange diffchange-inline">\fbox{</del>[K; M]\alpha \Leftrightarrow [K][M]\alpha <del class="diffchange diffchange-inline">} </del>\end{equation} </math><br /></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax ;}[K; M]\alpha \Leftrightarrow [K][M]\alpha <ins class="diffchange diffchange-inline"> </ins>\end{equation} </math><br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>and the inference rule  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>and the inference rule  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{R2}\dfrac{\alpha \Rightarrow \beta}{M\alpha \Rightarrow M\beta}  \end{equation} </math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{R2}\dfrac{\alpha \Rightarrow \beta}{M\alpha \Rightarrow M\beta}  \end{equation} </math></div></td></tr>
</table>
AndrzejSalwicki
http://lem12.uksw.edu.pl/index.php?title=Axiomatic_definitions_of_sublanguages_of_Loglan%2782&diff=1546&oldid=prev
AndrzejSalwicki: /* Characters */
2014-11-27T12:01:12Z
<p><span dir="auto"><span class="autocomment">Characters</span></span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← poprzednia wersja</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Wersja z 12:01, 27 lis 2014</td>
</tr><tr><td colspan="2" class="diff-lineno">Linia 87:</td>
<td colspan="2" class="diff-lineno">Linia 87:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax ;}\fbox{[K; M]\alpha \Leftrightarrow [K][M]\alpha } \end{equation} </math><br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax ;}\fbox{[K; M]\alpha \Leftrightarrow [K][M]\alpha } \end{equation} </math><br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>and the inference rule  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>and the inference rule  </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{R2}<del class="diffchange diffchange-inline">\fbox{</del>\dfrac{\alpha \Rightarrow \beta}{M\alpha \Rightarrow M\beta} <del class="diffchange diffchange-inline">}  </del>\end{equation} </math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{R2}\dfrac{\alpha \Rightarrow \beta}{M\alpha \Rightarrow M\beta} <ins class="diffchange diffchange-inline">  </ins>\end{equation} </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Now observe that the following formulas are equivalent<br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Now observe that the following formulas are equivalent<br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{align*}{}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{align*}{}</div></td></tr>
</table>
AndrzejSalwicki
http://lem12.uksw.edu.pl/index.php?title=Axiomatic_definitions_of_sublanguages_of_Loglan%2782&diff=1545&oldid=prev
AndrzejSalwicki: /* Characters */
2014-11-27T12:00:02Z
<p><span dir="auto"><span class="autocomment">Characters</span></span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← poprzednia wersja</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Wersja z 12:00, 27 lis 2014</td>
</tr><tr><td colspan="2" class="diff-lineno">Linia 87:</td>
<td colspan="2" class="diff-lineno">Linia 87:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax ;}\fbox{[K; M]\alpha \Leftrightarrow [K][M]\alpha } \end{equation} </math><br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax ;}\fbox{[K; M]\alpha \Leftrightarrow [K][M]\alpha } \end{equation} </math><br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>and the inference rule  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>and the inference rule  </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}<del class="diffchange diffchange-inline">\fbox{</del>\tag{R2}\dfrac{\alpha \Rightarrow \beta}{M\alpha \Rightarrow M\beta} }  \end{equation} </math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{R2}<ins class="diffchange diffchange-inline">\fbox{</ins>\dfrac{\alpha \Rightarrow \beta}{M\alpha \Rightarrow M\beta} }  \end{equation} </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Now observe that the following formulas are equivalent<br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Now observe that the following formulas are equivalent<br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{align*}{}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{align*}{}</div></td></tr>
</table>
AndrzejSalwicki
http://lem12.uksw.edu.pl/index.php?title=Axiomatic_definitions_of_sublanguages_of_Loglan%2782&diff=1544&oldid=prev
AndrzejSalwicki: /* Characters */
2014-11-27T11:59:06Z
<p><span dir="auto"><span class="autocomment">Characters</span></span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← poprzednia wersja</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Wersja z 11:59, 27 lis 2014</td>
</tr><tr><td colspan="2" class="diff-lineno">Linia 87:</td>
<td colspan="2" class="diff-lineno">Linia 87:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax ;}\fbox{[K; M]\alpha \Leftrightarrow [K][M]\alpha } \end{equation} </math><br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax ;}\fbox{[K; M]\alpha \Leftrightarrow [K][M]\alpha } \end{equation} </math><br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>and the inference rule  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>and the inference rule  </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{R2}\dfrac{\alpha \Rightarrow \beta}{M\alpha \Rightarrow M\beta}  \end{equation} </math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}<ins class="diffchange diffchange-inline">\fbox{</ins>\tag{R2}\dfrac{\alpha \Rightarrow \beta}{M\alpha \Rightarrow M\beta<ins class="diffchange diffchange-inline">} </ins>}  \end{equation} </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Now observe that the following formulas are equivalent<br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Now observe that the following formulas are equivalent<br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{align*}{}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{align*}{}</div></td></tr>
</table>
AndrzejSalwicki
http://lem12.uksw.edu.pl/index.php?title=Axiomatic_definitions_of_sublanguages_of_Loglan%2782&diff=1543&oldid=prev
AndrzejSalwicki: /* Characters */
2014-11-27T11:57:40Z
<p><span dir="auto"><span class="autocomment">Characters</span></span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← poprzednia wersja</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Wersja z 11:57, 27 lis 2014</td>
</tr><tr><td colspan="2" class="diff-lineno">Linia 83:</td>
<td colspan="2" class="diff-lineno">Linia 83:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>I.e. ''the execution of three instructions causes swap of the values of variables'' <math> c_1, c_2 </math>.<br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>I.e. ''the execution of three instructions causes swap of the values of variables'' <math> c_1, c_2 </math>.<br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>'''Proof''' uses two axioms of algorithmic logic: <br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>'''Proof''' uses two axioms of algorithmic logic: <br /></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax:=}[x:=\tau]\alpha \Leftrightarrow \alpha(x/\tau) \end{equation} </math> <br /></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax:=}<ins class="diffchange diffchange-inline">\fbox{</ins>[x:=\tau]\alpha \Leftrightarrow \alpha(x/\tau)<ins class="diffchange diffchange-inline">} </ins>\end{equation} </math> <br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>this axiom of assignment instruction reads: ''formula '' <math>\alpha(x/\tau)</math> '' holds iff after execution of instruction  '' <math>x:=\tau</math> ''formula  ''<math>\alpha</math> '' holds.''<br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>this axiom of assignment instruction reads: ''formula '' <math>\alpha(x/\tau)</math> '' holds iff after execution of instruction  '' <math>x:=\tau</math> ''formula  ''<math>\alpha</math> '' holds.''<br /></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax ;}[K; M]\alpha \Leftrightarrow [K][M]\alpha <del class="diffchange diffchange-inline"> </del>\end{equation} </math><br /></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax ;}<ins class="diffchange diffchange-inline">\fbox{</ins>[K; M]\alpha \Leftrightarrow [K][M]\alpha <ins class="diffchange diffchange-inline">} </ins>\end{equation} </math><br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>and the inference rule  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>and the inference rule  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{R2}\dfrac{\alpha \Rightarrow \beta}{M\alpha \Rightarrow M\beta}  \end{equation} </math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{R2}\dfrac{\alpha \Rightarrow \beta}{M\alpha \Rightarrow M\beta}  \end{equation} </math></div></td></tr>
</table>
AndrzejSalwicki
http://lem12.uksw.edu.pl/index.php?title=Axiomatic_definitions_of_sublanguages_of_Loglan%2782&diff=1542&oldid=prev
AndrzejSalwicki: /* Characters */
2014-11-27T11:33:07Z
<p><span dir="auto"><span class="autocomment">Characters</span></span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← poprzednia wersja</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Wersja z 11:33, 27 lis 2014</td>
</tr><tr><td colspan="2" class="diff-lineno">Linia 91:</td>
<td colspan="2" class="diff-lineno">Linia 91:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{align*}{}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{align*}{}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&(c_1 =a \land c_2=b)&            & \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&(c_1 =a \land c_2=b)&            & \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\<del class="diffchange diffchange-inline">Rightleftarrow </del>&(c_1 =a \land c_2=b \land c1=a)&            & \mbox{by propositional calculus} \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\<ins class="diffchange diffchange-inline">Leftrightarrow </ins>&(c_1 =a \land c_2=b \land c1=a)&            & \mbox{by propositional calculus} \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\<del class="diffchange diffchange-inline">Rightleftarrow </del>& [c_3:=c_1](c_3=a \land c_2 =b \land c_3=a) &      & \mbox{by Ax :=} \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\<ins class="diffchange diffchange-inline">Leftrightarrow </ins>& [c_3:=c_1](c_3=a \land c_2 =b \land c_3=a) &      & \mbox{by Ax :=} \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\<del class="diffchange diffchange-inline">Rightleftarrow </del>&  [c_3:=c_1][c_1:=c_2](c_3=a \land c_1 =b \land c_3=a) &      & \mbox{by Ax := and R2} \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\<ins class="diffchange diffchange-inline">Leftrightarrow </ins>&  [c_3:=c_1][c_1:=c_2](c_3=a \land c_1 =b \land c_3=a) &      & \mbox{by Ax := and R2} \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\<del class="diffchange diffchange-inline">Rightleftarrow </del>&  [c_3:=c_1; c_1:=c_2](c_3=a \land c_1 =b \land c_3=a) &      & \mbox{by Ax ;} \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\<ins class="diffchange diffchange-inline">Leftrightarrow </ins>&  [c_3:=c_1; c_1:=c_2](c_3=a \land c_1 =b \land c_3=a) &      & \mbox{by Ax ;} \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\<del class="diffchange diffchange-inline">Rightleftarrow </del>&  [c_3:=c_1; c_1:=c_2][c_2 :=c_3](c_2=a \land c_1 =b \land c_3=a) &      & \mbox{by Ax := and R2}\\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\<ins class="diffchange diffchange-inline">Leftrightarrow </ins>&  [c_3:=c_1; c_1:=c_2][c_2 :=c_3](c_2=a \land c_1 =b \land c_3=a) &      & \mbox{by Ax := and R2}\\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\<del class="diffchange diffchange-inline">Rightleftarrow </del>&  [c_3:=c_1; c_1:=c_2; c_2 :=c_3](c_2=a \land c_1 =b \land c_3=a) &      & \mbox{by Ax ;} \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\<ins class="diffchange diffchange-inline">Leftrightarrow </ins>&  [c_3:=c_1; c_1:=c_2; c_2 :=c_3](c_2=a \land c_1 =b \land c_3=a) &      & \mbox{by Ax ;} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\end{align*}  </math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\end{align*}  </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
</table>
AndrzejSalwicki
http://lem12.uksw.edu.pl/index.php?title=Axiomatic_definitions_of_sublanguages_of_Loglan%2782&diff=1541&oldid=prev
AndrzejSalwicki: /* Characters */
2014-11-27T11:31:28Z
<p><span dir="auto"><span class="autocomment">Characters</span></span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← poprzednia wersja</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Wersja z 11:31, 27 lis 2014</td>
</tr><tr><td colspan="2" class="diff-lineno">Linia 91:</td>
<td colspan="2" class="diff-lineno">Linia 91:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{align*}{}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{align*}{}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&(c_1 =a \land c_2=b)&            & \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&(c_1 =a \land c_2=b)&            & \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\<del class="diffchange diffchange-inline">Rightarrow </del>&(c_1 =a \land c_2=b \land c1=a)&            & \mbox{by propositional calculus} \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\<ins class="diffchange diffchange-inline">Rightleftarrow </ins>&(c_1 =a \land c_2=b \land c1=a)&            & \mbox{by propositional calculus} \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\<del class="diffchange diffchange-inline">Rightarrow </del>& [c_3:=c_1](c_3=a \land c_2 =b \land c_3=a) &      & \mbox{by Ax :=} \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\<ins class="diffchange diffchange-inline">Rightleftarrow </ins>& [c_3:=c_1](c_3=a \land c_2 =b \land c_3=a) &      & \mbox{by Ax :=} \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\<del class="diffchange diffchange-inline">Rightarrow </del>&  [c_3:=c_1][c_1:=c_2](c_3=a \land c_1 =b \land c_3=a) &      & \mbox{by Ax := and R2} \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\<ins class="diffchange diffchange-inline">Rightleftarrow </ins>&  [c_3:=c_1][c_1:=c_2](c_3=a \land c_1 =b \land c_3=a) &      & \mbox{by Ax := and R2} \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\<del class="diffchange diffchange-inline">Rightarrow </del>&  [c_3:=c_1; c_1:=c_2](c_3=a \land c_1 =b \land c_3=a) &      & \mbox{by Ax ;} \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\<ins class="diffchange diffchange-inline">Rightleftarrow </ins>&  [c_3:=c_1; c_1:=c_2](c_3=a \land c_1 =b \land c_3=a) &      & \mbox{by Ax ;} \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\<del class="diffchange diffchange-inline">Rightarrow </del>&  [c_3:=c_1; c_1:=c_2][c_2 :=c_3](c_2=a \land c_1 =b \land c_3=a) &      & \mbox{by Ax := and R2}\\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\<ins class="diffchange diffchange-inline">Rightleftarrow </ins>&  [c_3:=c_1; c_1:=c_2][c_2 :=c_3](c_2=a \land c_1 =b \land c_3=a) &      & \mbox{by Ax := and R2}\\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\<del class="diffchange diffchange-inline">Rightarrow </del>&  [c_3:=c_1; c_1:=c_2; c_2 :=c_3](c_2=a \land c_1 =b \land c_3=a) &      & \mbox{by Ax ;} \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\<ins class="diffchange diffchange-inline">Rightleftarrow </ins>&  [c_3:=c_1; c_1:=c_2; c_2 :=c_3](c_2=a \land c_1 =b \land c_3=a) &      & \mbox{by Ax ;} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\end{align*}  </math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\end{align*}  </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
</table>
AndrzejSalwicki
http://lem12.uksw.edu.pl/index.php?title=Axiomatic_definitions_of_sublanguages_of_Loglan%2782&diff=1540&oldid=prev
AndrzejSalwicki: /* Characters */
2014-11-27T11:29:29Z
<p><span dir="auto"><span class="autocomment">Characters</span></span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← poprzednia wersja</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Wersja z 11:29, 27 lis 2014</td>
</tr><tr><td colspan="2" class="diff-lineno">Linia 81:</td>
<td colspan="2" class="diff-lineno">Linia 81:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><big>Lemma</big><br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><big>Lemma</big><br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>(c_1=a \land c_2=b)\Rightarrow [c_3:=c_1; c_1:=c_2; c_2:=c_3](c_1=b \land c_2=a) </math><br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>(c_1=a \land c_2=b)\Rightarrow [c_3:=c_1; c_1:=c_2; c_2:=c_3](c_1=b \land c_2=a) </math><br /></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>I.e. ''the execution of three instructions causes swap of the values of variables'' <math> c_1, c_2 </math>.<del class="diffchange diffchange-inline">,</del>br /></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>I.e. ''the execution of three instructions causes swap of the values of variables'' <math> c_1, c_2 </math>.<ins class="diffchange diffchange-inline"><</ins>br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>'''Proof''' uses two axioms of algorithmic logic: <br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>'''Proof''' uses two axioms of algorithmic logic: <br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax:=}[x:=\tau]\alpha \Leftrightarrow \alpha(x/\tau) \end{equation} </math> <br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax:=}[x:=\tau]\alpha \Leftrightarrow \alpha(x/\tau) \end{equation} </math> <br /></div></td></tr>
</table>
AndrzejSalwicki
http://lem12.uksw.edu.pl/index.php?title=Axiomatic_definitions_of_sublanguages_of_Loglan%2782&diff=1539&oldid=prev
AndrzejSalwicki: /* Characters */
2014-11-27T11:28:54Z
<p><span dir="auto"><span class="autocomment">Characters</span></span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← poprzednia wersja</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Wersja z 11:28, 27 lis 2014</td>
</tr><tr><td colspan="2" class="diff-lineno">Linia 80:</td>
<td colspan="2" class="diff-lineno">Linia 80:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>One need not to guess. We have much better tool. <br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>One need not to guess. We have much better tool. <br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><big>Lemma</big><br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><big>Lemma</big><br /></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>(c_1=a \land c_2=b)\Rightarrow [c_3:=c_1; c_1:=c_2; c_2:=c_3](c_1=b \land c_2=a) </math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math>(c_1=a \land c_2=b)\Rightarrow [c_3:=c_1; c_1:=c_2; c_2:=c_3](c_1=b \land c_2=a) </math<ins class="diffchange diffchange-inline">><br /</ins>></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>I.e. ''the execution of three instructions causes swap of the values of variables'' <math> c_1, c_2 </math>.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>I.e. ''the execution of three instructions causes swap of the values of variables'' <math> c_1, c_2 </math>.<ins class="diffchange diffchange-inline">,br /></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>'''Proof''' uses two axioms of algorithmic logic: <br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>'''Proof''' uses two axioms of algorithmic logic: <br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax:=}[x:=\tau]\alpha \Leftrightarrow \alpha(x/\tau) \end{equation} </math> <br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>\begin{equation}\tag{Ax:=}[x:=\tau]\alpha \Leftrightarrow \alpha(x/\tau) \end{equation} </math> <br /></div></td></tr>
</table>
AndrzejSalwicki
http://lem12.uksw.edu.pl/index.php?title=Axiomatic_definitions_of_sublanguages_of_Loglan%2782&diff=1538&oldid=prev
AndrzejSalwicki: /* Characters */
2014-11-27T11:27:05Z
<p><span dir="auto"><span class="autocomment">Characters</span></span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← poprzednia wersja</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Wersja z 11:27, 27 lis 2014</td>
</tr><tr><td colspan="2" class="diff-lineno">Linia 78:</td>
<td colspan="2" class="diff-lineno">Linia 78:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Guess what will print this program.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Guess what will print this program.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>One need not to guess. We have much better tool.  </div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>One need not to guess. We have much better tool. <ins class="diffchange diffchange-inline"><br /></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><big>Lemma</big><br /></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><big>Lemma</big><br /></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>(c_1=a \land c_2=b)\Rightarrow [c_3:=c_1; c_1:=c_2; c_2:=c_3](c_1=b \land c_2=a) </math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>(c_1=a \land c_2=b)\Rightarrow [c_3:=c_1; c_1:=c_2; c_2:=c_3](c_1=b \land c_2=a) </math></div></td></tr>
</table>
AndrzejSalwicki