Logical Resolution Proofs and Exercise Solutions
By
Dr. Ismael AbdulSattar
1
Resolution
1)
The law says that it is a crime for an American to sell
weapons to hostel nations. The country Nono, an enemy
of American, has some missiles, and all of its missiles
were sold to it by Colonel West, Who is American.
Use resolution to proof that
"West is a criminal
"
Exercise
2
2) If you have the following sentence:
Exercise
Use resolution to proof that
"Curiosity killed Tuna
"
3
If a person is a female and is a parent, then this Pearson is someone's
mother.
∀
X
∃
y
((female(X) Λ parent (X)) → mother (X, Y))
Everyone has exactly one best friend.
∃
y
(best_friend(X, Y) Λ
∀
Z
(¬
equal (Z, Y) →
¬
best_friend (X, Y))
Alive means not dead.
∀
X:
∀
T:[ alive(X, T) →
¬
dead (X, T)] Λ [
¬
dead (X, T) → alive(X, T)
If someone dies, then he is dead at all later times.
∀
X:
∀
T1:
∀
T2: died (X, T1) Λ gt(T2,T1 ) → dead (X, T2))
No mortal lives longer than 150 years.
∀
X:
∀
T1:
∀
T2: mortal (X) Λ born (X, T1) Λ gt(T2-T1,150 ) → dead (X,
T2))
Answers
4
Answers
5
Now convert to CNF
Answers
6
A resolution proof that
"West is a criminal
"
Answers
7
Answers
8
Answers
9
This content provides exercises on logical resolution proofs and solutions, including proving that "West is a criminal" and resolving statements related to mortality, relationships, and more. It also covers converting statements to Conjunctive Normal Form (CNF).
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Presentation Transcript
By Dr. Ismael AbdulSattar 1
Exercise Resolution 1) The law says that it is a crime for an American to sell weapons to hostel nations. The country Nono, an enemy of American, has some missiles, and all of its missiles were sold to it by Colonel West, Who is American. Use resolution to proof that "West is a criminal" 2 C93734F252A1F5B0294E69D3A9A7AB8F
Exercise 2) If you have the following sentence: Use resolution to proof that "Curiosity killed Tuna" 3 C93734F252A1F5B0294E69D3A9A7AB8F
Answers If a person is a female and is a parent, then this Pearson is someone's mother. X y((female(X) parent (X)) mother (X, Y)) Everyone has exactly one best friend. y (best_friend(X, Y) Z ( equal (Z, Y) best_friend (X, Y)) Alive means not dead. X: T:[ alive(X, T) dead (X, T)] [ dead (X, T) alive(X, T) If someone dies, then he is dead at all later times. X: T1: T2: died (X, T1) gt(T2,T1 ) dead (X, T2)) No mortal lives longer than 150 years. X: T1: T2: mortal (X) born (X, T1) gt(T2-T1,150 ) dead (X, T2)) 4 C93734F252A1F5B0294E69D3A9A7AB8F
Answers 5 C93734F252A1F5B0294E69D3A9A7AB8F
Answers Now convert to CNF 6 C93734F252A1F5B0294E69D3A9A7AB8F
Answers A resolution proof that "West is a criminal" 7 C93734F252A1F5B0294E69D3A9A7AB8F
Answers 8 C93734F252A1F5B0294E69D3A9A7AB8F
Answers 9 C93734F252A1F5B0294E69D3A9A7AB8F
