📄 content-1-2-2.htm
字号:
<html>
<head>
<title>Untitled Document</title>
<meta http-equiv="Content-Type" content="text/html; charset=gb2312">
<style type="text/css">
<!--
.unnamed1 { font-size: 9pt; line-height: 15pt}
.unnamed2 { font-size: 10pt; font-weight: bold}
-->
</style>
</head>
<body background="IMAGE/di.gif">
<table width="100%" border="0" cellspacing="0" cellpadding="0">
<tr>
<td>
<p style="line-height: 150%" align="center"><font size="5"><b>范
式</b></font></p>
<p style="line-height: 150%"> 一个公式有很多的等价形式,但是有没有一个标准的形式呢?这就是十我们要介绍的公式的范式。
</p>
<p style="line-height: 150%"> 为介绍范式，先要介绍基本积和基本和的概念。此处用积表示<a href="content-1-1-2.htm#hequ">合取</a>，用和表示<a href="content-1-1-2.htm#xiqu">析取</a>
。<br>
</p>
<p style="line-height: 150%"><b>1、基本积</b>： 命题公式中的变元及变元否定之<font color="#0000FF">积</font>，称为基本<font color="#0000FF">积</font>。</p>
<p style="line-height: 150%" align="center">如：P、P<img border="0" src="image/hequ.gif" width="9" height="11">Q、<img border="0" src="image/fei.gif" width="10" height="5">P<img border="0" src="image/hequ.gif" width="9" height="11">Q、<img border="0" src="image/fei.gif" width="10" height="5">P<img border="0" src="image/hequ.gif" width="9" height="11"><img border="0" src="image/fei.gif" width="10" height="5">Q<img border="0" src="image/hequ.gif" width="9" height="11">P</p>
<p style="line-height: 150%"><b>2、基本和</b>： 命题公式中的变元及变元否定之<font color="#0000FF">和</font>，称为基本<font color="#0000FF">和</font>。
</p>
<p style="line-height: 150%" align="center">如：P、P<img border="0" src="image/xiqu.gif" width="9" height="15">Q、<img border="0" src="image/fei.gif" width="10" height="5">P<img border="0" src="image/xiqu.gif" width="9" height="15">Q、<img border="0" src="image/fei.gif" width="10" height="5">P<img border="0" src="image/xiqu.gif" width="9" height="15"><img border="0" src="image/fei.gif" width="10" height="5">Q<img border="0" src="image/xiqu.gif" width="9" height="15">P</p>
<p style="line-height: 150%" align="left"><b>3、虚合取式</b>：某个命题变元P和它的否定<img border="0" src="image/fei.gif" width="10" height="5">P在同一个基本<font color="#0000FF">积</font>中出现，称该基本积为虚合取式。否则称为<b>实合取式</b>。</p>
<p style="line-height: 150%" align="center">如：<img border="0" src="image/fei.gif" width="10" height="5">P<img border="0" src="image/hequ.gif" width="9" height="11"><img border="0" src="image/fei.gif" width="10" height="5">Q<img border="0" src="image/hequ.gif" width="9" height="11">P、<img border="0" src="image/fei.gif" width="10" height="5">P<img border="0" src="image/hequ.gif" width="9" height="11"><img border="0" src="image/fei.gif" width="10" height="5">Q<img border="0" src="image/hequ.gif" width="9" height="11">R</p>
<p style="line-height: 150%" align="left"><b>4、虚析取式</b>：某个命题变元P和它的否定<img border="0" src="image/fei.gif" width="10" height="5">P在同一个基本<font color="#0000FF">和</font>中出现，称该基本积为虚合取式。否则称为<b>实析取式</b>。</p>
<p style="line-height: 150%" align="center">如：<img border="0" src="image/fei.gif" width="10" height="5">P<img border="0" src="image/xiqu.gif" width="9" height="15"><img border="0" src="image/fei.gif" width="10" height="5">Q<img border="0" src="image/xiqu.gif" width="9" height="15">P、<img border="0" src="image/fei.gif" width="10" height="5">P<img border="0" src="image/xiqu.gif" width="9" height="15"><img border="0" src="image/fei.gif" width="10" height="5">Q<img border="0" src="image/xiqu.gif" width="9" height="15">R</p>
<p style="line-height: 150%"><b>5、析取范式</b>：与给定的命题公式F
等价的公式，如果是由<font color="#0000FF">基本积之和</font>组成，则称它是给定命题公式的析取范式。（公式的第一标准型）</p>
<p style="line-height: 150%" align="center">形如：A1 <img border="0" src="image/xiqu.gif" width="9" height="15">
A2 <img border="0" src="image/xiqu.gif" width="9" height="15"> A3 <img border="0" src="image/xiqu.gif" width="9" height="15">…<img border="0" src="image/xiqu.gif" width="9" height="15">
An，其中，Ai为基本<font color="#0000FF">积</font>。</p>
<p style="line-height: 150%" align="center">如:P<img src="image/dengtong.gif" width="16" height="9">Q<img src="image/dengjia.gif" width="17" height="9">(P<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">Q<img src="image/hequ.gif" width="9" height="11"><img src="image/fei.gif" width="10" height="5">P)</p>
<p style="line-height: 150%" align="left"><b>6、合取范式</b>：与给定的命题公式
F 等价的公式，如果是由<font color="#0000FF">基本和之积</font>组成，则称它是给定命题公式的合取范式。（公式的第二标准型）</p>
<p style="line-height: 150%" align="center">形如：A1 <img border="0" src="image/hequ.gif" width="9" height="11">
A2 <img border="0" src="image/hequ.gif" width="9" height="11"> A3 <img border="0" src="image/hequ.gif" width="9" height="11">…<img border="0" src="image/hequ.gif" width="9" height="11">
An，其中，Ai为基本<font color="#0000FF">和</font>。</p>
<p style="line-height: 150%" align="center">如:P<img src="image/dengtong.gif" width="16" height="9">Q<img src="image/dengjia.gif" width="17" height="9">(P<img src="image/xiqu.gif" width="9" height="15"><img src="image/fei.gif" width="10" height="5">Q)<img src="image/hequ.gif" width="9" height="11">(<img src="image/fei.gif" width="10" height="5">P<img src="image/xiqu.gif" width="9" height="15">Q)</p>
<p style="line-height: 150%" align="left">
任何一个公式都有与之相等价的析取范式和合取范式。但是命题的析取范式和合取范式都不具有不唯一，我们把运算符最少的析取范式和合取范式称为<b>最简析取范式</b>和<b>最简合取范式</b>。</p>
<p style="line-height: 150%" align="left">
求公式的析取范式和合取范式。<br>
步骤：</p>
<ol>
<li>
<p style="line-height: 150%" align="left">消去联结词<img border="0" src="image/yunhan.gif" width="15" height="9">、<img src="image/dengtong.gif" width="16" height="9">；</li>
<li>
<p style="line-height: 150%" align="left">将否定联结词深入到原子命题前面；</li>
<li>
<p style="line-height: 150%" align="left">利用分配律化为析取范式或合取范式。</li>
</ol>
<p style="line-height: 150%" align="left">例：求公式 <img border="0" src="image/fei.gif" width="10" height="5">(P<img border="0" src="image/xiqu.gif" width="9" height="15">Q)<img src="image/dengtong.gif" width="16" height="9">(P<img border="0" src="image/hequ.gif" width="9" height="11">Q)
的析取范式和合取范式。</p>
<p style="line-height: 150%" align="left"> </p>
<p style="line-height: 150%" align="left"><b>主范式</b></p>
<p style="line-height: 150%"> 命题的析取范式和合取范式都不具有不唯一，不方便比较，进一步引入主范式：
</p>
<p style="line-height: 150%"> 为介绍主范式先要介绍极小项和极大项的概念: <br>
</p>
<p style="line-height: 150%"><b>1、极小项：</b>在有
n 个命题变元的基本积中，若每个变元与其否定并不同时存在，且二者之一必出现一次且仅出现一次，则这种基本积称为极小项。
</p>
<p style="line-height: 150%" align="center">如：<img border="0" src="image/fei.gif" width="10" height="5">P<img border="0" src="image/hequ.gif" width="9" height="11"><img border="0" src="image/fei.gif" width="10" height="5">Q<img border="0" src="image/hequ.gif" width="9" height="11">R、P<img border="0" src="image/hequ.gif" width="9" height="11">Q<img border="0" src="image/hequ.gif" width="9" height="11">R
</p>
<p style="line-height: 150%" align="left">
则n个变元可以构成<img border="0" src="Image/2den.gif" width="13" height="12">个不同的极小项。如，3个变元P、Q、R可以构成8个极小项。
</p>
<p style="line-height: 150%" align="left">
我们把命题变元看成“1”，而命题变元的否定看成“0”，那么，若把P、Q、R按照一定的顺序排列下来可以把每个极小项依次对应于一个三位二进制数。如下：
</p>
<div align="center">
<center>
<table border="1" width="61%">
<tr>
<td width="25%" align="center">
<p align="center">极小项</td>
<td width="25%" align="center">二进制编码</td>
<td width="25%" align="center">对应的数</td>
<td width="25%" align="center">记作</td>
</tr>
<tr>
<td width="25%" align="center"><img border="0" src="image/fei.gif" width="10" height="5">P<img border="0" src="image/hequ.gif" width="9" height="11"><img border="0" src="image/fei.gif" width="10" height="5">Q<img border="0" src="image/hequ.gif" width="9" height="11"><img border="0" src="image/fei.gif" width="10" height="5">R</td>
<td width="25%" align="center">000</td>
<td width="25%" align="center">0</td>
<td width="25%" align="center"><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:-5.0pt"><!--[if gte vml 1]><v:shapetype
id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
<v:stroke joinstyle="miter"/>
<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"/>
<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"/>
</v:formulas>
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
<o:lock v:ext="edit" aspectratio="t"/>
</v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:15pt;
height:17.25pt' o:ole="">
<v:imagedata src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image001.wmz"
o:title=""/>
</v:shape><![endif]-->
</span><span style="mso-text-raise:-6.0pt"><img src="Image/m0.gif" v:shapes="_x0000_i1032" width="16" height="11"></span><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1032"
DrawAspect="Content" ObjectID="_1077123477">
</o:OLEObject>
</xml><![endif]-->
</span></td>
</tr>
<tr>
<td width="25%" align="center"><img border="0" src="image/fei.gif" width="10" height="5">P<img border="0" src="image/hequ.gif" width="9" height="11"><img border="0" src="image/fei.gif" width="10" height="5">Q<img border="0" src="image/hequ.gif" width="9" height="11">R</td>
<td width="25%" align="center">001</td>
<td width="25%" align="center">1</td>
<td width="25%" align="center"><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:-5.0pt"><img src="Image/m1.gif" v:shapes="_x0000_i1025" width="15" height="11"></span><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1031"
DrawAspect="Content" ObjectID="_1077123476">
</o:OLEObject>
</xml><![endif]-->
<span style="mso-text-raise:-6.0pt"><!--[if gte vml 1]><v:shape
id="_x0000_i1032" type="#_x0000_t75" style='width:15.75pt;height:18pt' o:ole="">
<v:imagedata src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image015.wmz"
o:title=""/>
</v:shape><![endif]-->
</span></span></td>
</tr>
<tr>
<td width="25%" align="center"><img border="0" src="image/fei.gif" width="10" height="5">P<img border="0" src="image/hequ.gif" width="9" height="11">
Q<img border="0" src="image/hequ.gif" width="9" height="11"><img border="0" src="image/fei.gif" width="10" height="5">R</td>
<td width="25%" align="center">010</td>
<td width="25%" align="center">2</td>
<td width="25%" align="center"><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 mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1025"
DrawAspect="Content" ObjectID="_1077123470">
</o:OLEObject>
</xml><![endif]-->
<span style="mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape
id="_x0000_i1026" type="#_x0000_t75" style='width:15.75pt;height:17.25pt'
o:ole="">
<v:imagedata src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image003.wmz"
o:title=""/>
</v:shape><![endif]-->
<img src="Image/m2.gif" v:shapes="_x0000_i1026" width="16" height="11"></span><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1026"
DrawAspect="Content" ObjectID="_1077123471">
</o:OLEObject>
</xml><![endif]-->
<span style="mso-text-raise:-6.0pt"><!--[if gte vml 1]><v:shape
id="_x0000_i1031" type="#_x0000_t75" style='width:15.75pt;height:18pt' o:ole="">
<v:imagedata src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image013.wmz"
⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -