Truth table

(1)

Unbounded Knowledge Acquisition Based Upon

Mutual Information in Dependent Questions

Tony C. Smith & Chris van de Molen

Department of Computer Science Waikato University

tcs@cs.waikato.ac.nz

(2)

 Motivation/background

 Representations of knowledge

(3)

(4)

Attribute vs. entity

Fruitbat Eagle Tiger Rock …

Is alive? T T T F

Flies? T T F F

Lays eggs? F T F F

…

(5)

Attribute vs. entity

Fruitbat Eagle Tiger Rock …

Is alive? 0.90 0.96 0.88 0.01

Flies? 0.85 0.97 0.04 0.22

Lays eggs? 0.20 0.91 0.00 0.01

…

YES, NO, SOMETIMES, USUALLY, MAYBE, SELDOM, RARELY, etc

(6)

 A measure of the information (i.e.

uncertainty) in an event ω whose

probability is p_ω can be expressed in bits as

I (ω) = - log₂ p_ω

 Entropy is the average information content

I (ω) = - p_ω log₂ p_ω

 Mutual information is the amount of information two events share

MI(X, Y) = I(x) + I(y) – [I(x) + I(y|x)]

(7)

Given:

P(A) = 1/32 P(B) = 1/64 P(B|A) = 1/2 P(A|B) = 1/4 Then:

I(A) = 5 I(B) = 6 I(A,B) = 1

MI(A,B) = 5 + 6 – (