https://mw.lojban.org/index.php?title=three-value_logic&feed=atom&action=history
three-value logic - Revision history
2024-03-29T15:43:21Z
Revision history for this page on the wiki
MediaWiki 1.38.4
https://mw.lojban.org/index.php?title=three-value_logic&diff=122968&oldid=prev
Gleki: /* The three assertions: */
2018-07-01T10:52:20Z
<p><span dir="auto"><span class="autocomment">The three assertions:</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:52, 1 July 2018</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l43">Line 43:</td>
<td colspan="2" class="diff-lineno">Line 43:</td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>!cai</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>!cai</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">!</del>(1,-1,-1)</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">|</ins>(1,-1,-1)</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">!</del>necessarily</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">|</ins>necessarily</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">|</del>sai</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">!</ins>sai</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|(1,0,0)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|(1,0,0)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|probably</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|probably</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">|</del>ru'e</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">!</ins>ru'e</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|(1,1,-1)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|(1,1,-1)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|possibly</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|possibly</div></td></tr>
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Gleki
https://mw.lojban.org/index.php?title=three-value_logic&diff=122967&oldid=prev
Gleki: /* by la xorxes: */
2018-07-01T10:52:06Z
<p><span dir="auto"><span class="autocomment">by la xorxes:</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:52, 1 July 2018</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l7">Line 7:</td>
<td colspan="2" class="diff-lineno">Line 7:</td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>!cai</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>!cai</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">!</del>(1,-1,-1)</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">|</ins>(1,-1,-1)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>!sai</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>!sai</div></td></tr>
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Gleki
https://mw.lojban.org/index.php?title=three-value_logic&diff=122966&oldid=prev
Gleki: /* by la xorxes: */
2018-07-01T10:51:58Z
<p><span dir="auto"><span class="autocomment">by la xorxes:</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:51, 1 July 2018</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l9">Line 9:</td>
<td colspan="2" class="diff-lineno">Line 9:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>!(1,-1,-1)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>!(1,-1,-1)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">|</del>sai</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">!</ins>sai</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|(1,0,0)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|(1,0,0)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">|</del>ru'e</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">!</ins>ru'e</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|(1,1,-1)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|(1,1,-1)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">|</del>cu'i</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">!</ins>cu'i</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|(0,1,-1)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|(0,1,-1)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">|</del>nai</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">!</ins>nai</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|(-1,0,1)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|(-1,0,1)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr>
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Gleki
https://mw.lojban.org/index.php?title=three-value_logic&diff=122965&oldid=prev
Gleki at 10:51, 1 July 2018
2018-07-01T10:51:19Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:51, 1 July 2018</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l64">Line 64:</td>
<td colspan="2" class="diff-lineno">Line 64:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>**The following truth tables are the return value for true, norje'u, and false, in that order. (The plus in parentheses means that it is plausible (for example) that the statement is true, and the minus, that it is plausible that the statement is false. The glosses are an elaboration of the glosses presented in the above paper.)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>**The following truth tables are the return value for true, norje'u, and false, in that order. (The plus in parentheses means that it is plausible (for example) that the statement is true, and the minus, that it is plausible that the statement is false. The glosses are an elaboration of the glosses presented in the above paper.)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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>{|class=wikitable</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>{|class=<ins style="font-weight: bold; text-decoration: none;">'</ins>wikitable<ins style="font-weight: bold; text-decoration: none;">'</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| (1, 1, 1)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| (1, 1, 1)</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l208">Line 208:</td>
<td colspan="2" class="diff-lineno">Line 208:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*This works very similarly to the traditional logical operators of possibility and necessity, i.e. ''it is possible that not ...'' = ''it is not necessary that ...'', etc. However, there are differences. ''It is possible that broda and it is possible that not broda'' in two-valued modal logic says nothing about the actual truth value of ''broda''. However, (taking AND(x, y) to be <nowiki>min(x, y]</nowiki> the truth-value of '''ge ru'e broda gi nairu'e broda''' is equivalent to the truth-value of '''cu'icai broda''', and the statement claims that the truth-value of '''broda''' must necessarily be '''norje'u''':</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*This works very similarly to the traditional logical operators of possibility and necessity, i.e. ''it is possible that not ...'' = ''it is not necessary that ...'', etc. However, there are differences. ''It is possible that broda and it is possible that not broda'' in two-valued modal logic says nothing about the actual truth value of ''broda''. However, (taking AND(x, y) to be <nowiki>min(x, y]</nowiki> the truth-value of '''ge ru'e broda gi nairu'e broda''' is equivalent to the truth-value of '''cu'icai broda''', and the statement claims that the truth-value of '''broda''' must necessarily be '''norje'u''':</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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>{|class=wikitable</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>{|class=<ins style="font-weight: bold; text-decoration: none;">'</ins>wikitable<ins style="font-weight: bold; text-decoration: none;">'</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| broda</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| broda</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l237">Line 237:</td>
<td colspan="2" class="diff-lineno">Line 237:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*:There are 3<sup>9</sup> = 19,683 possible binary operators. A simple and relatively intuitive definition for AND is the minimum of the two predicates and for OR is the maximum of the two predicates:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*:There are 3<sup>9</sup> = 19,683 possible binary operators. A simple and relatively intuitive definition for AND is the minimum of the two predicates and for OR is the maximum of the two predicates:</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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>{|class=wikitable</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>{|class=<ins style="font-weight: bold; text-decoration: none;">'</ins>wikitable<ins style="font-weight: bold; text-decoration: none;">'</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| '''x'''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| '''x'''</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l280">Line 280:</td>
<td colspan="2" class="diff-lineno">Line 280:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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>{|</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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 style="font-weight: bold; text-decoration: none;">class='wikitable'</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| '''x'''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| '''x'''</div></td></tr>
</table>
Gleki
https://mw.lojban.org/index.php?title=three-value_logic&diff=122964&oldid=prev
Gleki: /* (work in progress) */
2018-07-01T10:48:25Z
<p><span dir="auto"><span class="autocomment">(work in progress)</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:48, 1 July 2018</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l61">Line 61:</td>
<td colspan="2" class="diff-lineno">Line 61:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*I don't get it. What are your axes?</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*I don't get it. What are your axes?</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>**This proposal is from [http://groups.yahoo.com/group/lojban/message/3218 A discussion of trivalent logic in the summer of 2000]. See also [http://www.aymara.org The Aymara Language] and [http://www.aymara.org/biblio/igr/igr.html The paper describing Aymara suffixes in terms of trivalent logic]. A detailed description of trivalent logic begins at the section labeled "4.1" in [http://www.aymara.org/biblio/igr/igr4.html Chapter IV: The Logical Suffixes of the Aymara Language] of that paper.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>**This proposal is from [http://groups.yahoo.com/group/lojban/message/3218 A discussion of trivalent logic in the summer of 2000]. See also [http://www.aymara.org The Aymara Language] and [http://www.aymara.org/biblio/igr/igr.html The paper describing Aymara suffixes in terms of trivalent logic]. A detailed description of trivalent logic begins at the section labeled "4.1" in [http://www.aymara.org/biblio/igr/igr4.html Chapter IV: The Logical Suffixes of the Aymara Language] of that paper.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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>**In brief, trivalent logic uses, in addition to the standard two truth values of TRUE and FALSE, a third value (neither true nor false, both true and false, etc.), which might be called ''ina'', after the Aymara, or <del style="font-weight: bold; text-decoration: none;">[[</del>norje'u<del style="font-weight: bold; text-decoration: none;">]] </del>in Lojban. True is represented by 1, norje'u by 0, and false by -1. The notation P = (p1, p2, p3) for a unary operator P means that P(1) = p1, P(0) = p2, P(-1) = p3. It relates the truth value (one of 1, 0, or -1) of an operand to the truth value of a claim (P, in this case) about the operand. p1 represents the truth of P(x) when x is known to be true (1). p2 represents the truth value of P(x) when x is known to be neither-true-nor-false (0, or ''ina''). p3 represents the truth value of P(x) if x is known to be false (-1).</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>**In brief, trivalent logic uses, in addition to the standard two truth values of TRUE and FALSE, a third value (neither true nor false, both true and false, etc.), which might be called ''ina'', after the Aymara, or <ins style="font-weight: bold; text-decoration: none;">{{vlapoi|</ins>norje'u<ins style="font-weight: bold; text-decoration: none;">}} </ins>in Lojban. True is represented by 1, norje'u by 0, and false by -1. The notation P = (p1, p2, p3) for a unary operator P means that P(1) = p1, P(0) = p2, P(-1) = p3. It relates the truth value (one of 1, 0, or -1) of an operand to the truth value of a claim (P, in this case) about the operand. p1 represents the truth of P(x) when x is known to be true (1). p2 represents the truth value of P(x) when x is known to be neither-true-nor-false (0, or ''ina''). p3 represents the truth value of P(x) if x is known to be false (-1).</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>**The following truth tables are the return value for true, norje'u, and false, in that order. (The plus in parentheses means that it is plausible (for example) that the statement is true, and the minus, that it is plausible that the statement is false. The glosses are an elaboration of the glosses presented in the above paper.)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>**The following truth tables are the return value for true, norje'u, and false, in that order. (The plus in parentheses means that it is plausible (for example) that the statement is true, and the minus, that it is plausible that the statement is false. The glosses are an elaboration of the glosses presented in the above paper.)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
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Gleki
https://mw.lojban.org/index.php?title=three-value_logic&diff=122963&oldid=prev
Gleki: /* by la xorxes: */
2018-07-01T10:47:59Z
<p><span dir="auto"><span class="autocomment">by la xorxes:</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:47, 1 July 2018</td>
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Gleki
https://mw.lojban.org/index.php?title=three-value_logic&diff=122962&oldid=prev
Gleki: /* The three assertions: */
2018-07-01T10:47:50Z
<p><span dir="auto"><span class="autocomment">The three assertions:</span></span></p>
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Gleki
https://mw.lojban.org/index.php?title=three-value_logic&diff=122961&oldid=prev
Gleki at 10:47, 1 July 2018
2018-07-01T10:47:40Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:47, 1 July 2018</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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 think {{vlapoi|cai}}, {{vlapoi|ru'e}} and {{vlapoi|nai}} are the easiest to accept. (-1,0,1) is the most obvious generalization of {{vlapoi|nai}} from binary. (1,-1,-1) corresponds to the strongest assertion (certainty or necessity, depending on what system we use it on) so it has to be {{vlapoi|cai}}. (1,1,-1) is possibility or a weak assertion, so I think {{vlapoi|ru'e}} fits well. Now, (1,0,0) is also an assertion, but not as strong as certainty, something like "this is how it is, but I give no guarantees". I think {sai} can work for that.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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 think {{vlapoi|cai}}, {{vlapoi|ru'e}} and {{vlapoi|nai}} are the easiest to accept. (-1,0,1) is the most obvious generalization of {{vlapoi|nai}} from binary. (1,-1,-1) corresponds to the strongest assertion (certainty or necessity, depending on what system we use it on) so it has to be {{vlapoi|cai}}. (1,1,-1) is possibility or a weak assertion, so I think {{vlapoi|ru'e}} fits well. Now, (1,0,0) is also an assertion, but not as strong as certainty, something like "this is how it is, but I give no guarantees". I think {<ins style="font-weight: bold; text-decoration: none;">{vlapoi|</ins>sai<ins style="font-weight: bold; text-decoration: none;">}</ins>} can work for that.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>And finally, {{vlapoi|cu'i}} is for neutral. (0,1,-1) is not absolutely neutral, it is uncertainty with a bent towards assertion, but it is the closest to neutral and we do need it to generate others, so {{vlapoi|cu'i}} has to be it.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>And finally, {{vlapoi|cu'i}} is for neutral. (0,1,-1) is not absolutely neutral, it is uncertainty with a bent towards assertion, but it is the closest to neutral and we do need it to generate others, so {{vlapoi|cu'i}} has to be it.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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>With those 5 it is possible to generate all 27 unary operators, with at most three of them. For example, (0,0,1) is {<del style="font-weight: bold; text-decoration: none;">naisai</del>}, (-1,1,-1) is {{vlapoi|cu'i|cai}}, (0,0,0) is {{vlapoi|sai|ru'e|cu'i}} (among several possibilities), etc.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>With those 5 it is possible to generate all 27 unary operators, with at most three of them. For example, (0,0,1) is {<ins style="font-weight: bold; text-decoration: none;">{vlapoi|nai|sai}</ins>}, (-1,1,-1) is {{vlapoi|cu'i|cai}}, (0,0,0) is {{vlapoi|sai|ru'e|cu'i}} (among several possibilities), etc.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Only 8 of the 27 need three basic functions, the rest can be formed from just two.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Only 8 of the 27 need three basic functions, the rest can be formed from just two.</div></td></tr>
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Gleki
https://mw.lojban.org/index.php?title=three-value_logic&diff=122960&oldid=prev
Gleki at 10:46, 1 July 2018
2018-07-01T10:46:30Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:46, 1 July 2018</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l208">Line 208:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*** For each n, the role of a single rotation + a single exchange can be played by n-1 exchanges, provided that they are connected -- there is a path from any one value to any other using the exchanges provided. The 3-value case (replace the rotation by an exchange) works because every pair of exchanges over three values is connected. The two value case - using only negation -- fits better with this generalization than with the universal 3-function scheme. Any rotation that does not share a prime factor with n can be used as the rotation (a rotation with a span of 1 can be defined). In any case, only one identification is needed. >|8}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*** For each n, the role of a single rotation + a single exchange can be played by n-1 exchanges, provided that they are connected -- there is a path from any one value to any other using the exchanges provided. The 3-value case (replace the rotation by an exchange) works because every pair of exchanges over three values is connected. The two value case - using only negation -- fits better with this generalization than with the universal 3-function scheme. Any rotation that does not share a prime factor with n can be used as the rotation (a rotation with a span of 1 can be defined). In any case, only one identification is needed. >|8}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*For a given unary operator, its <u>opposite</u> is the result of applying '''nai''' to it, or of multiplying it by -1. For example, the opposite of '''ru'e''' (1, 1, -1) is '''ru'enai''' (-1, -1, 1). Also, its "antonym" is the result of applying it to '''nai''', or of reversing its order. For example, the antonym of '''ru'e''' (1, 1, -1) is '''nairu'e''' (-1, 1, 1).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*For a given unary operator, its <u>opposite</u> is the result of applying '''nai''' to it, or of multiplying it by -1. For example, the opposite of '''ru'e''' (1, 1, -1) is '''ru'enai''' (-1, -1, 1). Also, its "antonym" is the result of applying it to '''nai''', or of reversing its order. For example, the antonym of '''ru'e''' (1, 1, -1) is '''nairu'e''' (-1, 1, 1).</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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>*Unary operators are commutative ('''[<del style="font-weight: bold; text-decoration: none;">[cairu'e|</del>cairu'e]<del style="font-weight: bold; text-decoration: none;">]</del>sai''' = '''cai[<del style="font-weight: bold; text-decoration: none;">[ru'esai|</del>ru'esai]<del style="font-weight: bold; text-decoration: none;">]</del>''') and so the opposite of the antonym is the same as the antonym of the opposite ('''[<del style="font-weight: bold; text-decoration: none;">[nairu'e|</del>nairu'e]<del style="font-weight: bold; text-decoration: none;">]</del>nai''' = '''nai<del style="font-weight: bold; text-decoration: none;">[</del>[ru'enai<del style="font-weight: bold; text-decoration: none;">|ru'enai]</del>]'''), and the opposite-antonym of the opposite-antonym is the operator itself ('''nai[<del style="font-weight: bold; text-decoration: none;">[nairu'enai|</del>nairu'enai]<del style="font-weight: bold; text-decoration: none;">]</del>nai''' = '''[<del style="font-weight: bold; text-decoration: none;">[nainai|</del>nainai<del style="font-weight: bold; text-decoration: none;">]</del>]ru'e<del style="font-weight: bold; text-decoration: none;">[</del>[nainai<del style="font-weight: bold; text-decoration: none;">|nainai]</del>]''' = '''ru'e'''). '''ru'e''' and '''cai''' are opposite antonyms.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>*Unary operators are commutative ('''<ins style="font-weight: bold; text-decoration: none;"><nowiki></ins>[cairu'e]<ins style="font-weight: bold; text-decoration: none;"></nowiki></ins>sai''' = '''cai<ins style="font-weight: bold; text-decoration: none;"><nowiki></ins>[ru'esai]<ins style="font-weight: bold; text-decoration: none;"></nowiki></ins>''') and so the opposite of the antonym is the same as the antonym of the opposite ('''<ins style="font-weight: bold; text-decoration: none;"><nowiki></ins>[nairu'e]<ins style="font-weight: bold; text-decoration: none;"></nowiki></ins>nai''' = '''nai<ins style="font-weight: bold; text-decoration: none;"><nowiki></ins>[ru'enai]<ins style="font-weight: bold; text-decoration: none;"></nowiki></ins>'''), and the opposite-antonym of the opposite-antonym is the operator itself ('''nai<ins style="font-weight: bold; text-decoration: none;"><nowiki></ins>[nairu'enai]<ins style="font-weight: bold; text-decoration: none;"></nowiki></ins>nai''' = '''<ins style="font-weight: bold; text-decoration: none;"><nowiki></ins>[nainai]ru'e[nainai]<ins style="font-weight: bold; text-decoration: none;"></nowiki></ins>''' = '''ru'e'''). '''ru'e''' and '''cai''' are opposite antonyms.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*It is possible to move '''nai''' around, but every operator that it crosses must be replaced by its opposite-antonym. '''cainai''' -> '''nairu'enai nai''' -> '''nairu'e''', etc.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*It is possible to move '''nai''' around, but every operator that it crosses must be replaced by its opposite-antonym. '''cainai''' -> '''nairu'enai nai''' -> '''nairu'e''', etc.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*This works very similarly to the traditional logical operators of possibility and necessity, i.e. ''it is possible that not ...'' = ''it is not necessary that ...'', etc. However, there are differences. ''It is possible that broda and it is possible that not broda'' in two-valued modal logic says nothing about the actual truth value of ''broda''. However, (taking AND(x, y) to be <nowiki>min(x, y]</nowiki> the truth-value of '''ge ru'e broda gi nairu'e broda''' is equivalent to the truth-value of '''cu'icai broda''', and the statement claims that the truth-value of '''broda''' must necessarily be '''norje'u''':</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*This works very similarly to the traditional logical operators of possibility and necessity, i.e. ''it is possible that not ...'' = ''it is not necessary that ...'', etc. However, there are differences. ''It is possible that broda and it is possible that not broda'' in two-valued modal logic says nothing about the actual truth value of ''broda''. However, (taking AND(x, y) to be <nowiki>min(x, y]</nowiki> the truth-value of '''ge ru'e broda gi nairu'e broda''' is equivalent to the truth-value of '''cu'icai broda''', and the statement claims that the truth-value of '''broda''' must necessarily be '''norje'u''':</div></td></tr>
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Gleki
https://mw.lojban.org/index.php?title=three-value_logic&diff=122959&oldid=prev
Gleki at 10:44, 1 July 2018
2018-07-01T10:44:57Z
<p></p>
<a href="https://mw.lojban.org/index.php?title=three-value_logic&diff=122959&oldid=122958">Show changes</a>
Gleki