# Fit3080 Tutorial

**Topics:**Quantification, First-order logic, Predicate logic

**Pages:**12 (1992 words)

**Published:**March 12, 2013

FIT3080: Intelligent Systems

Ramesh Kumar Ayyasamy

Sunway Campus

ramesh .kumar@monash.edu

My tutorial ground rules

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During tutorial hours, you are allowed only to

- do the given tutorial tasks as mentioned in Moodle.

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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.

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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

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

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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”

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

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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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