Quantitive Measures of Uncertainty

Question 1

Give a formal definition of a syllogism

Answer 1

X is a Y, All Y are Z, Therefore, X is a Z

Question 2

What does W represent?

Answer 2

The finite set of all possible worlds

Question 3

What does w* represent?

Answer 3

The true world

Question 4

What is the fundamental property of monotonicity?

Answer 4

That a proposition B is as believeable if not more believable than proposition A where B is a more general statement then A

Question 5

What is the fundamental property of additivity?

Answer 5

If a proposition C is the disjunct of the propositions A and B then C = A + B

Question 6

What is the definition of additivity for an uncertainty measure C where A ∩ B ≠ Ø?

Question 7

What is the definition of additivity for an uncertainty measure C where A ∩ B = Ø?

Question 8

Define the uncertainty measure function

Question 9

What is the value of

Answer 9

1

Question 10

What is the value of

Answer 10

0

Question 11

Define the General Form of the sub-additive measure

Question 12

Define the sub-additive measure for A∩B = Ø

Question 13

Define the maxitive measure

Question 14

What is the Maxitive Measure a special case of?

Answer 14

Sub-additive measures

Question 15

Define the General Form of the super-additive measure

Question 16

Define the super-additive measure for A∩B = Ø

Question 17

Define the minimal measure

Question 18

What is the minimal measure a special case of?

Answer 18

The super-additive measure

Question 19

Define the random variable function X

Answer 19

X: W →

Question 20

What does

Answer 20

The measurement domain

Question 21

Define the random set function R

Answer 21

R: W → 2^