CS 371 - Introduction to Artificial Intelligence
Homework #6
Due: Thursday 12/5 at the beginning of class Note: Work is to be done individually.
Truth tables, validity, and satisfiability: R&N 6.1
Equivalence rules: R&N 6.3 a,c,e,g
Abbreviate Smoke, Fire, etc. as S, F, etc.
Hint: Simplify expressions (and reduce truth table work) using equivalence
rules.
Propositional reasoning: R&N 6.5
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.)
Models: R&N 6.7
implies, entails, derives:
Describe the difference between "implies", "entails", and "derives".
What word describes an inference procedure that entails what it derives?
What word describes an inference procedure that derives what it entails?