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Massachusetts Institute of Technology
16.410 Principles of Automated Reasoning
and Decision Making
Problem Set #8
Due:Session18
Propositional Logic
Objectives
In this problem set we develop your understanding of logical
representation and reasoning.
First, you will learn to count the number of
models that satisfy a given sentence.
Next, you will determine the
satisfiability of a sentence using truth tables and equivalence rules.
Finally,
you will derive the truth of a statement based on a knowledgebase of
sentences.
Readings
AIMA Chapter 7.
Problem 1 – Planner Implementation (40 pts in Pset #7).
Submit your solution to Problem 3 “Cleaning up Rooms” described in
Problem Set #7.
Recall that this problem involved encoding a planning
problem and executing it on a planner.
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View Full DocumentProblem 2 – Problem #7.5, AIMA
(15 points)
In this problem, you will consider a vocabulary with four propositions, A,
B, C, and D.
How many models are there for the following sentences?
Justify each answer.
a.)
()
( )
C
B
B
A
∧
∨
∧
b.)
B
A
∨
c.)
C
B
A
⇔
⇔
Problem 3 – Problem #7.8, AIMA (25 points)
Decide whether each of the following sentences is valid, unsatisfiable, or
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 Fall '05
 BrianWilliams

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