CS 662: AI Programming
Homework #4: Logic
Assigned: October 11
Due: October 18.
To turn in: Typed or clearly handwritten answers to the questions throughout
the homework. (Note: if you have messy handwriting, please type your
answers. If we can't read what you've written, we can't grade it.)
In this problem, you'll use propositional logic to reason about a
simple world containing two robots and a charger. The problem is for
each robot to determine whether it should move to the charger or not.
- R1: Robot1 is on.
- R2: Robot 2 is on.
- ChR1: Robot 1 is at the charger.
- ChR2: Robot 2 is at the charger.
- lowR1: Robot 1 has low power.
- lowR2: Robot 2 has low power.
- moveChR1: Robot 1 should move onto the charger.
- moveChR2: Robot 2 should move onto the charger.
A. (5 points). Write propositional logic sentences for each of the
following English-language sentences, using the abbreviations above.
- If robot 1 is off, then robot 2 is off.
- If robot 2 is off, then it will be located on the charger, and if
it is not off, then robot 2 will not be located on the charger.
- If robot 1 is off, then it will be located on the charger, and if
it is not off, then robot 1 will not be located on the charger.
- If Robot 1 is on, and its power is low, then it should move to
- Robot 1's power is low.
- Robot 2 is on.
B. (10 points) Convert each of the sentences above to CNF.
C. (5 points) Use resolution with refutation to prove that
Robot 1 should move to the charger.
(10 points) Translate each of the following sentences into first-order logic,
using the following predicates: Student(x), likes(x,y), worksAt(x,y),
- All the students like Bart.
- Unless a person is a student, that person works at the power plant.
- Marge Simpson has exactly two children: Bart and Lisa.
- There is someone is Springfield who is liked by everyone.
- Every student likes himself/herself.