 CS 371 - Introduction to Artificial Intelligence Homework #6

Due: Thursday 12/5 at the beginning of class
Note: Work is to be done individually.
1. Truth tables, validity, and satisfiability: R&N 6.1
2. Equivalence rules: R&N 6.3 a,c,e,g

3. Abbreviate Smoke, Fire, etc. as S, F, etc.
Hint: Simplify expressions (and reduce truth table work) using equivalence rules.
4. Propositional reasoning: R&N 6.5

5. Use the following propositional symbols to reduce your writing:
• P: The unicorn is mythical.
• Q: The unicorn is immortal.
• R: The unicorn is a mammal.
• S: The unicorn has a horn.
• T: The unicorn is magical.
If the proposition can be proven, provide a step-by-step proof. If it cannot be proven, demonstrate this by providing an appropriate model.
Hint: A simple proof method is refutation (also known as proof by contradiction, see R&N p. 280).
Another hint: You can use the equivalence rules of Exercise 6.2 to construct equivalence sentences helpful to your proof. Each equivalence can be written as a conjunction of two implications, each of which can be used with modus ponens. (Contraposition may be especially useful depending on your approach.)
6. Models: R&N 6.7
7. implies, entails, derives:
1. Describe the difference between "implies", "entails", and "derives".
2. What word describes an inference procedure that entails what it derives?
3. What word describes an inference procedure that derives what it entails?