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 AI 2010

2. Outline  Motivation/background  Representations of knowledge

4. Truth table Attribute vs. entity FruitbatEagleTigerRock… Is alive?TTTF Flies?TTFF Lays eggs?FTFF …

5. Multivalued truth table Attribute vs. entity FruitbatEagleTigerRock… Is alive?0.900.960.880.01 Flies?0.850.970.040.22 Lays eggs?0.200.910.000.01 … YES, NO, SOMETIMES, USUALLY, MAYBE, SELDOM, RARELY, etc

6. Mutual Information  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) = - log 2 p ω  Entropy is the average information content I (ω) = - p ω log 2 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. Mutual information example 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 – (