Soundness of GMP Need to show that p1',,pm',(p1A..Apm→q)上q0 provided that p=p:for all i Lemma:For any definite clause p,we have p=p by Ul 1.(p1∧..∧Pn→q=(p1A..∧Pn→q)0=(p10∧..Apn8→q) 2.p'.,pn'p'A..Apn'卡p1'8A.∧pn'0 3.From 1 and 2,ge follows by ordinary Modus Ponens Chapter 9 16
Soundness of GMP Need to show that p1 0 , . . . , pn 0 , (p1 ∧ . . . ∧ pn ⇒ q) |= qθ provided that pi0θ = piθ for all i Lemma: For any definite clause p, we have p |= pθ by UI 1. (p1 ∧ . . . ∧ pn ⇒ q) |= (p1 ∧ . . . ∧ pn ⇒ q)θ = (p1θ ∧ . . . ∧ pnθ ⇒ qθ) 2. p10, . . . , pn0 |= p10 ∧ . . . ∧ pn0 |= p10θ ∧ . . . ∧ pn0θ 3. From 1 and 2, qθ follows by ordinary Modus Ponens Chapter 9 16
Example knowledge base The law says that it is a crime for an American to sell weapons to hostile nations.The country Nono,an enemy of America,has some missiles,and all of its missiles were sold to it by Colonel West,who is American. Prove that Col.West is a criminal Chapter 9 17
Example knowledge base The law says that it is a crime for an American to sell weapons to hostile nations. The country Nono, an enemy of America, has some missiles, and all of its missiles were sold to it by Colonel West, who is American. Prove that Col. West is a criminal Chapter 9 17