# CS 1571: Homework 6

## Propositional Logic (Chapter 7): Paper Problems (100 pts)

Assigned: October 28, 2008

Due: November 4, 2008

#### 1. Entailment (25 pts)

Let KB be a knowledge base consisting of the following sentence:
- (A OR C) AND (B OR (NOT C))

  Prove that (A OR B) holds using the truth-table approach.

  Grading Criteria: To get full credit, you first need to show the truth table, making sure you have columns for all intermediate steps. You then need to explain how you interpret the truth table to prove (A OR B), either by highlighting rows, or by using one or two sentences to explain the process.

  #### 2. Resolution (75 pts)

  Knowledge Base:

- Either (I have a sweet tooth and I like chocolate) or (I like chocolate and I like cake)

  Rules:

- If I like cake, then I also like Danish.
- If I like Danish, that implies I have a sweet tooth.
- If I have a sweet tooth and I like chocolate, then I am a chocoholic.

  Goal: I am a chocoholic

  (a) Convert these sentences to propositional logic.

  (b) Put the resulting sentences into Conjunctive Normal Form.

  (c) Using proof by refutation and resolution as the single inference rule, show the resolution proof that proves or disproves the goal.

  Grading Criteria: For part(c), you can either use a graph or show the resolution process step by step. Even if the first two steps are wrong, you can get credit, if we think you did the correct resolution.