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了解一下简单析取式和简单合取式,简单析取式说白了就是有限个命题变项或者他们的否定用符号v连接起来的式子,比如p,¬p,pvq,pv¬q等,简单合取式类似,但它用的符号是Λ。析取范式简单来说就是几个简单析取式的组合,合取范式类似。
而主合取和主析取略微有些不同,主析取是由极小项及符号v组成,极小项就是简单合取式,说白了主析取就是由符号v连接几个简单合取式组成,且他的每一个构成单位(极小项)的命题变项的个数都是一样的,举个例子:(pΛq)v(qΛr),这不是主析取,因为这个式子总共有三个命题变项,p,q,r,第一个单元pΛq并未包含r,而第二个式子qΛr里也没有p,不完整,不能成为主析取范式,这个时候我们想要让他成为主析取范式则要进行操作,对第一个式子加上缺少的项r,怎么加呢?答案是将第一个式子用(pΛq)Λ(rv¬r)代替,因为极小项对应成真赋值交上一个rv¬r原式并未改变,然后合理运用分配律变换式子,使其变成主析取范式。主合取刚好相反,主合取对应极大项,成假赋值,对应如下:
主析取–极小项(简单合取式)–成真赋值(式子Λ(xv¬x))
析——小——真
主合取–极大项(简单析取式)–成假赋值(式子v(xΛ¬x))
合——大——假
析取范式变成主析取的时候结果出现的项对应的角码即其成真赋值,未出现的为成假赋值,合取范式变成主合取的结果出现的项对应的角码即其成假赋值,未出现的是成真赋值。(n个项对应2的n次方种情况,其二进制角码转换成十进制数字即下标,如000对应m。,001对应m1等)