CS 371
Introduction to Artificial Intelligence
Homework #4
Due: Tuesday 9/26
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?
Using GSAT:
Convert the following sentences into conjunctive normal form (CNF):
P implies Q
(not P) implies ((not Q) and R)
(Q or R) implies S
S implies T
Use GSAT to test whether or not this CNF KB does not entail:
P
S
T
Could GSAT be used to prove that propositional logic formulas are entailed
by a CNF KB? Why (and how) or why not?
Be sure to include all input and output files in your README file.
Derive a CNF formula which, when satisfied provides a test pattern to check
whether D is stuck at 0 in the following circuit:
Use GSAT to find a satisfying assignment to the above formula. Hand in
your input and output file. How would you then use this satisfying assignment
to test for the fault?
GSAT and 3CNF problem difficulty: R&N 6.15 a,b,d,f. See the
GSAT
How-To guide for information about the
gtime script.