内容发布更新时间 : 2025/6/26 8:09:45星期一 下面是文章的全部内容请认真阅读。
p(x)?S(x,f(x)) Q(x) P(w)?B(w)
I. 子句变量标准化后, 最终的子句集为：
p(x)?S(x,f(x)) Q(y)
P(w)?B(w)
(2) 参见课本P122 A. 消去蕴涵符符号：
(?x)[~P(x)?[?y[~P(y)?P(f(x,y))]?~?y[~Q(x,y)?P(y)]]] B. 减少否定符号的辖域:
(?x)[~P(x)?[?y[~P(y)?P(f(x,y))]??y[Q(x,y)?~P(y)]]] C. 变量标准化:
(?x)[~P(x)?[?y[~P(y)?P(f(x,y))]??w[Q(x,w)?~P(w)]]] D. 消去存在量词:
(?x)[~P(x)?[?y[~P(y)?P(f(x,y))]?[Q(x,g(x))?~P(g(x))]]] E. 化为前束型:
(?x)(?y)[~P(x)?[[~P(y)?P(f(x,y))]?[Q(x,g(x))?~P(g(x))]]] F. 把母式化为合取范式:
(?x)(?y)[~P(x)?~P(y)?P(f(x,y))]?[~P(x)?Q(x,g(x))]?[~P(x)?~P(g(x))]]
G. 消去全称量词:
[~P(x)?~P(y)?P(f(x,y))]?[~P(x)?Q(x,g(x))]?[~P(x)?~P(g(x))]]
H. 消去合取词:~P(x)?~P(y)?P(f(x,y))
~P(x)?Q(x,g(x)) ~P(x)?~P(g(x)) I. 更改变量名:
~P(x1)?~P(y)?P(f(x1,y)) ~P(x2)?Q(x2,g(x2))
~P(x3)?~P(g(x3))
4.7 把下面的表达式转化成子句形式
（1）((?x)[p(x)]?(?x)[Q(x)]?(?x)[P(x)?Q(x)]
（2）(?x)[P(x)]?(?x)[(?z)[Q(x,z)]?(?z)[R(x,y,z)]]
（3）(?x)[P(x)?(?y)[(?z)[Q(x,y)]?~(?z)[R(y,x)]]] [解]
(1) ((?x)P(x)?(?x)Q(x))?(?x)(P(x)?Q(x)) ?((?x)P(x)?(?x)Q(x))?(?x)(P(x)?Q(x)) (?(?x)P(x)??(?x)Q(x))?(?x)(P(x)?Q(x))
((?x)?P(x)?(?x)?Q(x))?(?x)(P(x)?Q(x)) ((?x)?P(x)?(?x)?Q(x))?(?z)(P(z)?Q(z))
((?x)?P(x)?(?y)?Q(y))?(P(a)?Q(a)) (?x)(?y)(?P(x)??Q(y))?(P(a)?Q(a))) (?P(x)??Q(y))?(P(a)?Q(a))
(?P(x)?P(a)?Q(a))??Q(y))?(P(a)?Q(a))
则子句集为
9
S?{?P(x)?P(a)?Q(a)),?Q(y))?(P(a)?Q(a)} (2) (?x)P(x)?(?x)[(?z)Q(x,z)?(?z)R(x,y,z)]
(?y)((?x)P(x)?(?x)[(?z)Q(x,z)?(?z)R(x,y,z)]) (?y)(?(?x)P(x)?(?x)[(?z)Q(x,z)?(?z)R(x,y,z)])
(?y)((?x)?P(x)?(?x)[(?z)Q(x,z)?(?z)R(x,y,z)])
(?y)((?x)?P(x)?(?t)[(?z)Q(t,z)?(?u)R(t,y,u)])