1. Knowledge Representation
a) There are no crazy UMB students.
x (UMBStudent(x)  Crazy(x))
b) All computer scientists are either rich or crazy, but not both.
x (CS(x)  [Rich(x)  Crazy(x)]  [Rich(x)  Crazy(x)] )
c) All UMB students except one are intelligent.
x (UMBStudent(x)  Intelligent(x))  x,y (UMBStudent(x)  UMBStudent(y)  Identical(x, y)  Intelligent(x)  Intelligent(y))
d) Jerry and Betty have the same friends.
x ([Friends(Betty, x)  Friends(Jerry, x)]  [Friends(Jerry, x)  Friends(Betty, x)])
e) No mouse is bigger than an elephant.
x,y (Mouse(x)  Elephant(y)  BiggerThan(x, y))
October 18, 2018
Introduction to Artificial Intelligence Lecture 14: Knowledge Representation & Reasoning III

2. Rules of Inference x P(x) Universal instantiation __________
 P(c) if cU
Universal instantiation
P(c) for an arbitrary cU
___________________
 x P(x)
Universal generalization
x P(x)
______________________
 P(c) for some element cU
Existential instantiation
P(c) for some element cU
____________________
 x P(x)
Existential generalization
October 18, 2018
Introduction to Artificial Intelligence Lecture 14: Knowledge Representation & Reasoning III

3. Rules of Inference Example: Every UMB student is a genius.
George is a UMB student.
Therefore, George is a genius.
U(x): “x is a UMB student.”
G(x): “x is a genius.”
October 18, 2018
Introduction to Artificial Intelligence Lecture 14: Knowledge Representation & Reasoning III

4. Rules of Inference The following steps are used in the argument:
Step 1: x (U(x)  G(x)) Hypothesis
Step 2: U(George)  G(George) Univ. instantiation using Step 1
Step 3: U(George) Hypothesis
Step 4: G(George) Modus ponens using Steps 2 & 3
x P(x)
__________
 P(c) if cU
Universal instantiation
October 18, 2018
Introduction to Artificial Intelligence Lecture 14: Knowledge Representation & Reasoning III