The Independent Choice Logic for modeling multiple agents under uncertainty David Poole Presented by Mei Huang Mar. 18,2005

Outline  Knowledge Representation  ICL Overview  ICL Semantics  ICL Influence  Discussion

Outline  Knowledge Representation  ICL Overview  ICL Semantics  ICL Influence  Discussion

“a bridge between logical representation and belief networks”

Q?Q?

Discussion  What do you think of the author’s claim that using disjunction to handle uncertainty is a stupid thing?  From the view point of representation, disjunction is not that bad, at least, it provides compact representations than ICL. E.g, “e  a 1 v …v a n ” in ICL needs n expressions.

Outline  Knowledge Representation  ICL Overview  ICL Semantics  ICL Influence  Discussion

Note: each item in F, i.e, each rules has an associated probability. E.g, for the first rule, the probability is P(f | c 1, b 1 ). This probability is different from the probability of a possible world.

Q?Q?

Discussion  How to cast the student-take-course domain problem into ICL?  Choice Space C={{L 1,L 2,L 3 },{High,Normal,Easy}} Facts F={Grade=A  IQ=L 3 ^ Difficulty=Easy; Grade=B  IQ=L 2 ^ Difficulty=High; ……} Give P 0 (L 1 ), P 0 (L 2 ), P 0 (L 3 ), P 0 (High), P 0 (Normal), P 0 (Easy)

Outline  Knowledge Representation  ICL Overview  ICL Semantics  ICL Influence  Discussion

Q?

Discussion  Why it looks so straight forward to map a decision tree to the rules of ICL?  The logical part of ICL focuses on attributes’ values, not attributes. ICL’s Fact set F interprets CPDs of BLP or LoPRM.

Q?

 How to translate this BN into ICL? 8  It is better to redraw the graph as 8 belief networks as follows: …… Because ICL’s rules are defined on the value level. Discussion BurglaryearthQuake Alarm B=trueQ=true A=true

are mutually exclusive

Outline  Knowledge Representation  ICL Overview  ICL Semantics  ICL Influence  Discussion

Discussion  In the diagram in slide15, why the arrows are uni-directional? Can they be made bi- directional?  What can ICL buy us? I.e, is this explicit bridge between logic and decision theory necessary or is the gap between the two enlarged imaginarily by the author? (when we deal with decision projects, logic is usually embodied implicitly in the program)