PROBLEM 6: RESOLUTION - REFUTATION (10 POINTS] Consider the following sentences in our knowledge base: 1. Snuggles is a puppy 2. Mauryn is a dog lover. 3. All puppies are dogs. 4. If any puppy follows directions, that puppy is good. 5. There is a dog that follows directions. 6. If any dog follows directions, Snuggles follows directions. 7. Whenever a dog lover finds a dog, if the dog is good, the dog lover adopts the dog. 8. Mauryn finds Snuggles. Use the following conventions: Puppy(x) x is a puppy. Dog(x) = x is a dog. Good(x) x is good. Doglover(x) -x is a dog lover. Follows Directions(x) x follows directions. Finds(x, y) - finds y Adopts(x, y) - x adopts y The above knowledge base can be translated into Conjunctive Normal Form as follows: 1. Puppy(Snuggles) 2. DogLover(Mauryn) 3. -Puppy(x) V Dog(x) 4. -Puppy(x) V-FollowsDirections(x) V Good(x) 5. Dog(OtherDog) A FollowsDirections(OtherDog) 6. Dog(x) V-Follows Directions(x) V Follows Directions(Snuggles) 7. -Finds(x, y) V-DogLover(x) V-Dogly) V-Goodly) V Adopts(x, y) 8. Finds(Mauryn, Snuggles) Use resolution-refutation to prove that Mauryn adopts Snuggles by filling in the rest of the table below. In the Number column, write the number of the sentence in the KB. In the sentence column, write the resulting sentence you are adding to the KB. In the Resolution and Substitution column, write which two sentences you are resolving together, and what you are substituting for the variables in the two sentences, if necessary. Number Sentence Resolution and Substitution PROBLEM 6: RESOLUTION - REFUTATION (10 POINTS] Consider the following sentences in our knowledge base: 1. Snuggles is a puppy 2. Mauryn is a dog lover. 3. All puppies are dogs. 4. If any puppy follows directions, that puppy is good. 5. There is a dog that follows directions. 6. If any dog follows directions, Snuggles follows directions. 7. Whenever a dog lover finds a dog, if the dog is good, the dog lover adopts the dog. 8. Mauryn finds Snuggles. Use the following conventions: Puppy(x) x is a puppy. Dog(x) = x is a dog. Good(x) x is good. Doglover(x) -x is a dog lover. Follows Directions(x) x follows directions. Finds(x, y) - finds y Adopts(x, y) - x adopts y The above knowledge base can be translated into Conjunctive Normal Form as follows: 1. Puppy(Snuggles) 2. DogLover(Mauryn) 3. -Puppy(x) V Dog(x) 4. -Puppy(x) V-FollowsDirections(x) V Good(x) 5. Dog(OtherDog) A FollowsDirections(OtherDog) 6. Dog(x) V-Follows Directions(x) V Follows Directions(Snuggles) 7. -Finds(x, y) V-DogLover(x) V-Dogly) V-Goodly) V Adopts(x, y) 8. Finds(Mauryn, Snuggles) Use resolution-refutation to prove that Mauryn adopts Snuggles by filling in the rest of the table below. In the Number column, write the number of the sentence in the KB. In the sentence column, write the resulting sentence you are adding to the KB. In the Resolution and Substitution column, write which two sentences you are resolving together, and what you are substituting for the variables in the two sentences, if necessary. Number Sentence Resolution and Substitution