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<p style="line-height: 150%" align="center"><font size="4"><b>命 题 公 式</b></font> </p>
<p style="line-height: 150%"><b>命题表达式</b> <br>
由命题变元和 <a href="content-1-1-2.htm">联结词</a>（包括圆括号）组成的表达式称为命题表达式。又称为字符串 。
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<p style="line-height: 150%">在命题逻辑的研究中，人们感兴趣的不是全部的这种字符串，而是某一类字符串，这一类字符串称为命题公式，又常称为合式公式 。
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<p style="line-height: 150%"><b>原子公式：</b> 单个命题变元和命题常元叫做原子公式。
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<p style="line-height: 150%"><b>合式公式定义</b>： <br>
当且仅当按下列规则生成的公式：
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(1)单个原子命题是一个合式公式；<br>
(2)如果A是一个合式公式，则<img src="image/fei.gif" width="10" height="5">A也是一个合式公式；
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(3)如果A和B是合式公式，则(A<img src="image/xiqu.gif" width="9" height="15">B)，(A<img src="image/hequ.gif" width="9" height="11">B），(A<img src="image/yunhan.gif" width="15" height="9">B)和(A<img src="image/dengtong.gif" width="16" height="9">B)都是合式公式；<br>
(4)经过有限次使用规则（l），（2）和（3），从而得到的由命题变元、联结词和圆括号所组成的字符串，是合式公式。
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<p style="line-height: 150%">
若公式A由n个不同的命题变元构成，则可记为<span style="mso-text-raise:-6.0pt"><span lang="EN-US" style="font-size:10.5pt;mso-bidi-font-size:
12.0pt;font-family:"Times New Roman";mso-fareast-font-family:宋体;mso-font-kerning:
1.0pt;mso-ansi-language:EN-US;mso-fareast-language:ZH-CN;mso-bidi-language:
AR-SA"><!--[if gte vml 1]><v:shapetype
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<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0"/>
<v:f eqn="sum @0 1 0"/>
<v:f eqn="sum 0 0 @1"/>
<v:f eqn="prod @2 1 2"/>
<v:f eqn="prod @3 21600 pixelWidth"/>
<v:f eqn="prod @3 21600 pixelHeight"/>
<v:f eqn="sum @0 0 1"/>
<v:f eqn="prod @6 1 2"/>
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<img src="Image/conten1.gif" v:shapes="_x0000_i1025" width="92" height="15"> <span style="mso-text-raise: -6.0pt; font-size: 10.5pt; mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA" lang="EN-US">. <!--[if gte mso 9]><xml>
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<p style="line-height: 150%"><b> 真值表的构造</b> </p>
<p style="line-height: 150%"> 若公式A由n个不同的命题变元构成，则A的真值表由n+1列，<span lang="EN-US" style="font-size:10.5pt;mso-bidi-font-size:
12.0pt;font-family:"Times New Roman";mso-fareast-font-family:宋体;mso-font-kerning:
1.0pt;mso-ansi-language:EN-US;mso-fareast-language:ZH-CN;mso-bidi-language:
AR-SA"><span style="mso-text-raise:-2.0pt"><!--[if gte vml 1]><v:shapetype
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<v:f eqn="sum @0 1 0"/>
<v:f eqn="sum 0 0 @1"/>
<v:f eqn="prod @2 1 2"/>
<v:f eqn="prod @3 21600 pixelWidth"/>
<v:f eqn="prod @3 21600 pixelHeight"/>
<v:f eqn="sum @0 0 1"/>
<v:f eqn="prod @6 1 2"/>
<v:f eqn="prod @7 21600 pixelWidth"/>
<v:f eqn="sum @8 21600 0"/>
<v:f eqn="prod @7 21600 pixelHeight"/>
<v:f eqn="sum @10 21600 0"/>
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<span style="font-size:10.5pt;mso-bidi-font-size:
12.0pt;font-family:"Times New Roman";mso-fareast-font-family:宋体;mso-font-kerning:
1.0pt;mso-ansi-language:EN-US;mso-fareast-language:ZH-CN;mso-bidi-language:
AR-SA" lang="EN-US">+1行。<br>
如：公式<img src="image/fei.gif" width="10" height="5">(P<img src="image/xiqu.gif" width="9" height="15"><img src="image/fei.gif" width="10" height="5">R)<img src="image/hequ.gif" width="9" height="11">(Q<img src="image/xiqu.gif" width="9" height="15"><img src="image/fei.gif" width="10" height="5">P)的真值表 </p>
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<td width="11%" align="center">P</td>
<td width="12%" align="center">Q</td>
<td width="12%" align="center">R</td>
<td width="65%" align="center"><img src="image/fei.gif" width="10" height="5">(P<img src="image/xiqu.gif" width="9" height="15"><img src="image/fei.gif" width="10" height="5">R)<img src="image/hequ.gif" width="9" height="11">(Q<img src="image/xiqu.gif" width="9" height="15"><img src="image/fei.gif" width="10" height="5">P) </td>
</tr>
<tr>
<td width="11%" align="center">0</td>
<td width="12%" align="center">0</td>
<td width="12%" align="center">0</td>
<td width="65%" align="center">0</td>
</tr>
<tr>
<td width="11%" align="center">0</td>
<td width="12%" align="center">0</td>
<td width="12%" align="center">1</td>
<td width="65%" align="center">1</td>
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<tr>
<td width="11%" align="center">0</td>
<td width="12%" align="center">1</td>
<td width="12%" align="center">0</td>
<td width="65%" align="center">0</td>
</tr>
<tr>
<td width="11%" align="center">0</td>
<td width="12%" align="center">1</td>
<td width="12%" align="center">1</td>
<td width="65%" align="center">1</td>
</tr>
<tr>
<td width="11%" align="center">1</td>
<td width="12%" align="center">0</td>
<td width="12%" align="center">0</td>
<td width="65%" align="center">0</td>
</tr>
<tr>
<td width="11%" align="center">1</td>
<td width="12%" align="center">0</td>
<td width="12%" align="center">1</td>
<td width="65%" align="center">0</td>
</tr>
<tr>
<td width="11%" align="center">1</td>
<td width="12%" align="center">1</td>
<td width="12%" align="center">0</td>
<td width="65%" align="center">0</td>
</tr>
<tr>
<td width="11%" align="center">1</td>
<td width="12%" align="center">1</td>
<td width="12%" align="center">1</td>
<td width="65%" align="center">0</td>
</tr>
</table>
</center>
</div>
<p style="line-height: 150%"> *<b>真值表相同的两个公式称为等价公式</b> </p>
<p style="line-height: 150%"> </p>
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<div align="center"> <img src="IMAGE/yuancheng_2.gif" width="100" height="69"></div>
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<p style="line-height: 150%"> </p>
<p style="line-height: 150%"> </p><p align="right"><b><a href="contentFrame-mulu.htm"><<back</a></b>
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