Fit3080 Tutorial

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  • Topic: Quantification, First-order logic, Predicate logic
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  • Published : March 12, 2013
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Information Technology

FIT3080: Intelligent Systems
Ramesh Kumar Ayyasamy
Sunway Campus

ramesh .kumar@monash.edu

My tutorial ground rules
1

During tutorial hours, you are allowed only to
- do the given tutorial tasks as mentioned in Moodle.

2

During tutorial hours, you are not allowed to
- not allowed to use Facebook, YouTube or any such activities which is not related to tutorial.

- not allowed to use mobile phones or chatting with your girl friends or boy friends.
- not to make loud noise.

2

Today’s Tasks – Tutorial 5
Knowledge representation
1. Exercise 6: First Order Logic
2. Exercise 7: Equivalence
3. Exercise 8: Unification
4. Exercise 9, 10: Resolution refutation

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Knowledge representation with Logic
Limitation on propositional logic


Propositional logic can only handle TRUE, FALSE and has “No capability to handle Uncertainty”, which is present in probability theory



It conveys only TRUE or FALSE of the world, but “does not considers objects that has properties such as size, weight, color, nor their relationships between objects”



No shortcuts or lacks expressiveness to describe the lots of activities happening around.



First-order logic address the two limitations: objects and shortcuts Refer, unit 7 in: https://www.ai-class.com/course/video/quizquestion/28

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Exercise 6: First-Order Logic

 First-Order Logic (FOL) is expressive to represent a good deal of our common sense knowledge.
 Quantifiers used here are :  (For all),  x (there exists and x such that or For some x)

• Logical Operators used here are :

 , , , , 

 Example for First-order logic: “All kings are persons” can be written as x King (x)  Person (x) .
“For all x, if x is a king, then x is a person.”, where x is a variable.  Example for First-order logic: “ King John has a crown on his head” can be written as  x Crown (x)  OnHead (x, John)
  appears to be the natural connective to use with ,   appears to be the natural connective to use with   The two quantifiers ( - universal, -existential) are closely connected with each other, through negation.

for example: “Everyone likes ice cream” means that there is no one who does not like ice cream, represented as :
x Likes (x, IceCream) is equivalent to   x  Likes(x , IceCream) 5

Exercise 6: First Order Logic
Question: Represent the following sentences in first-order logic: (a) “A computer system is intelligent, if it can perform a task which, if performed by a human, requires intelligence."
(b) “A formula whose main connective is a  is equivalent to some formula whose main connective is a  ."

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Question: Represent the following sentences in first-order logic: (a) “A computer system is intelligent, if it can perform a task which, if performed by a human, requires intelligence."
Solution:
There are several interpretations to this sentence and we discuss four of its interpretation. The following predicate calculus representations depict some of these interpretations.
i. ∀x {COMPUTER-SYSTEM(x) 

y [ TASK(y)  PERFORM(x, y) 
{PERFORM(HUMAN, y )  REQUIRES-INTELLIGENCE(HUMAN)}]
 INTELLIGENT(x)}}
English translation: “For all x such that x is a COMPUTER SYSTEM, and for which conditions 1-3 are fulfilled, then x is INTELLIGENT." Where conditions 1-3 are:

1. There exists a y such that y is a TASK, and
2. x PERFORMs y , and
3. if a human performs y then the human REQUIRES INTELLIGENCE. 7

Question: Represent the following sentences in first-order logic: (a) “A computer system is intelligent, if it can perform a task which, if performed by a human, requires intelligence."
Solution:

ii. ∀x {COMPUTER-SYSTEM(x) 
y [ TASK(y)  PERFORM(x, y) 
{PERFORM(HUMAN, y )  REQUIRES-INTELLIGENCE(HUMAN, y)}]
 INTELLIGENT(x)}
English translation: similar to the previous one, but now an explicit reference to y has been added to the REQUIRES-INTELLIGENCE predicate, to...
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