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some notes for the final exam =)

some notes for the final exam =). 1 st . A bout the final exam. Your final exam will contain 7 Questions , The first question is a True/False Question. Other 6 questions are mix from all chapters. Don’t forget that “chapter 1” is not included at the final exam.

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some notes for the final exam =)

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  1. some notes for the final exam =)

  2. 1st . A bout the final exam • Your final exam will contain 7 Questions , The first question is a True/False Question. Other 6 questions are mix from all chapters. • Don’t forget that “chapter 1” is not included at the final exam. • You are free to use the translator in the final exam. • If there wasn’t enough space to your answer you can complete it back of the paper.

  3. 2nd. A Little bit practice for the final exam • You have a sheets a bout some chapters . You can make some practice on it. • Do not forget to practice lectures slides Examples. • Examples that given Here are about the other chapters witch you didn’t get any sheet a bout it.

  4. Q1:Translate facts into prepositional logic and prove. A is on the right of B: RAB B is on the left of A: LBA C is on the top of B: TCB C is on the top of A: TCA If A is on the right of B, then B is on the left of A: R1: RAB ⇒ LBA If C is on the top of B which is on the left of A, then it is not on the top of A. R2:TCB ⋀ LBA⇒⌉TCA

  5. Q1:Translate facts into prepositional logic and prove, Cont… • Rules • R1: RAB ⇒ LBA , R2:TCB ⋀ LBA⇒⌉TCA • Fact  (knowing that RAB and TCB) • F1: RAB ,F2: TCB • Prove (⌉TCA ) F1 & R1 modus ponens gives F3: LBA F2 & F3 and-introduction gives F4:TCB ⋀LBA F4 & R2 modus ponens gives conclusion ⌉TCA

  6. Q2: Represent statements using first order logic. • Predicates: Bigger(x,y), Apple(x), Red(x), Delicious(x) • All red apples are delicious. • x, Apple(x) ⋀ Red(x) ⇒ Delicious(x) • Every delicious apple is bigger than some red apple. • x, y: Apple(x) ⋀ Delicious(x) ⇒ Apple(y) ⋀ Red(y) ⋀ Bigger(x,y) • x, y: Apple(x) ⋀ Delicious(x) ⋀ Apple(y) ⋀ Red(y) ⇒ Bigger(x,y)

  7. Q3: Give the most general unifier if it exists • P(A,A,B) and P(x,y,z): {x/A, y/A, z/B} • Q(I,H(A,B)) and Q(H(x,x),I): No unifier (x cannot bind to both A and B). • Older(Mother(y),y) and older(Mother(x),Maya): {y/Maya, x/Maya} • Knows(Father(y),y) and Knows(x,x): No unifier.

  8. Q4: Write down logical representations suitable for use with GMP • Horses, cows and pigs are mammals: Horse(x)  Mammal(x) Cow(x)  Mammal(x) Pig(x)  Mammal(x) • An offspring of a horse is a horse: Offspring(x,y)  Horse(y)  Horse(x) • Bluebeard is a horse: Horse (BlueBread) • Bluebeard is Charlie’s parent: Parent (BlueBread, Charlie) • Offspring and parent are inverse relations: Offspring(y, x)  Parent (x,y) Parent (x,y)  Offspring(y, x) • Every mammal has a parent: Mammal(x)  Parent(G(x), x) where G is Skolem function

  9. Hope To you the Best In your exam Good Luck

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