Problem 1 (4 points):

Read Chapter 7 of the text and define, in your own words, the term knowledge focusing on the difference between it and mere data. Also give two examples of real-world prblems that require knowledge (again as opposed to data) to solve, and are not mentioned in Chapter 7. Justify your answers.

According to Princeton's Cognitive Science Department, knowledge is the psychological result of perception, reasoning, and learning. Using this definition, data is a subset of knowledge. Scientists and other professionals often use a combination of perception, reasoning, and learning to generate data. Knowledge is different in that it enables an agent (human or intelligent machine) to create more knowledge using the same processes. Data alone cannot do this. Note that knowledge can be either explicit (formal and codified, e.g. a FOL knowledge base) or tacit (informal, e.g. insight). Two examples: software project management and deciding what to bring on a camping trip.

Problem 2 (6 points):

Part A:

1. Valid and Satisfiable
2. Satisfiable
3. Satisfiable

Part B:

1. (P ∨ R) ∧ (¬Q ∨ R)
2. (P ∨ Q) ∧ (P ∨ R)
3. (P ∨ Q) ∧ (¬P ∨ ¬Q) ∧ (¬P ∨ S) ∧ (Q ∨ S)

Part C: You can prove that the sprite lives in a tree and that it is small. It is not possible to prove that it is a fairy based on the information provided.

Part D: Proving that the sprite is small.

Result of step 1: Translating into propositional logic

1. “If a sprite is a fairy then it has wings” becomes: f → w
2. “If a sprite is not a fairy then it is mortal and does not have wings” becomes: ¬f → m ∧ ¬w
3. “If a sprite is either winged or mortal, then it lives in a tree” becomes: w ∨ m → t
4. “A sprite is small if it lives in a tree” becomes: t → s

Result of step 2: Converting into CNF

1. ¬f ∨ w
2. (f ∨ m) ∧ (f ∨ ¬w)
3. (¬w ∨ t) ∧ (¬m ∨ t)
4. ¬t ∨ s

Step 3: Proof by resolution (contradiction)
First list the clauses (disjunctions) from our knowledge base:

1. ¬f ∨ w
2. f ∨ m
3. f ∨ ¬w
4. ¬w ∨ t
5. ¬m ∨ t
6. ¬t ∨ s

7. ¬s