归结推理法证明问题A1 = (∃x)(P(x)∧(∀y)(R(x,y)→L(x,y)))A2 = (∀x)(P(x)→(∀y)(Q(y)→┐L(x,y)))B = ┐(∃x)(∀y)(R(y,x)∧Q(x))用归结推理法证明A1∧A2 => B请一定要用归结推理法
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/12 06:49:45
![归结推理法证明问题A1 = (∃x)(P(x)∧(∀y)(R(x,y)→L(x,y)))A2 = (∀x)(P(x)→(∀y)(Q(y)→┐L(x,y)))B = ┐(∃x)(∀y)(R(y,x)∧Q(x))用归结推理法证明A1∧A2 => B请一定要用归结推理法](/uploads/image/z/3628536-24-6.jpg?t=%E5%BD%92%E7%BB%93%E6%8E%A8%E7%90%86%E6%B3%95%E8%AF%81%E6%98%8E%E9%97%AE%E9%A2%98A1+%3D+%28%26%238707%3Bx%29%28P%28x%29%E2%88%A7%28%26%238704%3By%29%28R%28x%2Cy%29%E2%86%92L%28x%2Cy%29%29%29A2+%3D+%28%26%238704%3Bx%29%28P%28x%29%E2%86%92%28%26%238704%3By%29%28Q%28y%29%E2%86%92%E2%94%90L%28x%2Cy%29%29%29B+%3D+%E2%94%90%28%26%238707%3Bx%29%28%26%238704%3By%29%28R%28y%2Cx%29%E2%88%A7Q%28x%29%29%E7%94%A8%E5%BD%92%E7%BB%93%E6%8E%A8%E7%90%86%E6%B3%95%E8%AF%81%E6%98%8EA1%E2%88%A7A2+%3D%3E+B%E8%AF%B7%E4%B8%80%E5%AE%9A%E8%A6%81%E7%94%A8%E5%BD%92%E7%BB%93%E6%8E%A8%E7%90%86%E6%B3%95)
归结推理法证明问题A1 = (∃x)(P(x)∧(∀y)(R(x,y)→L(x,y)))A2 = (∀x)(P(x)→(∀y)(Q(y)→┐L(x,y)))B = ┐(∃x)(∀y)(R(y,x)∧Q(x))用归结推理法证明A1∧A2 => B请一定要用归结推理法
归结推理法证明问题
A1 = (∃x)(P(x)∧(∀y)(R(x,y)→L(x,y)))
A2 = (∀x)(P(x)→(∀y)(Q(y)→┐L(x,y)))
B = ┐(∃x)(∀y)(R(y,x)∧Q(x))
用归结推理法证明A1∧A2 => B
请一定要用归结推理法
归结推理法证明问题A1 = (∃x)(P(x)∧(∀y)(R(x,y)→L(x,y)))A2 = (∀x)(P(x)→(∀y)(Q(y)→┐L(x,y)))B = ┐(∃x)(∀y)(R(y,x)∧Q(x))用归结推理法证明A1∧A2 => B请一定要用归结推理法
证明:
(1) ∃x(P(x)∧ ∀y(R(x,y)→L(x,y))) P
(2) P(a)∧ ∀y( R(a,y)→L(a,y) ) ES(1)
(3) ∀y( R(a,y)→L(a,y) ) T(2)I
(4) ∀x(P(x)→∀y(Q(y)→┐L(x,y)) ) P
(5) P(a)→∀y( Q(y)→┐L(a,y) ) US(4)
(6) P(a) T(2)I
(7) ∀y( Q(y)→┐L(a,y) ) T(5)(6)I
(8) R(a,b)→L(a,b) US(3)
(9) Q(b)→┐L(a,b) US(7)
(10) L(a,b)→┐Q(b) T(9)E
(11) R(a,b)→┐Q(b) T(8)(10)I
(12) ┐(R(a,b)∧Q(b) ) T(11)E
(13) ∃y┐(R(y,b)∧Q(b) ) EG(12)
(14) ∀x∃y┐(R(y,x)∧Q(x) ) UG(13)
(15) ┐∃yx∀y(R(y,x)∧Q(x) ) T(14)E