Page 137 - DCAP310_INTRODUCTION_TO_ARTIFICIAL_INTELLIGENCE_AND_EXPERT_SYSTEMS

Unit 7: Probabilistic Reasoning

a nonzero value and let Y be a similar set for M . Then to get a new belief function M from the Notes
2 3
combination of M and M beliefs in and we do:
1 2
M = Σ M (X) M (y)/1-∑ M (X) M (y)
3 X∩ Y=Z 1 2 X∩ Y= φ 1 2
Stanford Certainty Factor Algebra

This approach was used in MYCIN for first time. It is based on Several Observations. Here Facts
and the outcome of rules are given confidence factor between -1 and +1

+1 means fact is known to be true.
-1 means fact is known to be false.
Here, the knowledge content of the rules is more important than the algebra of confidences
holding the system together. In this approach, confidence measures correspond to informal
assessments by humans such as “it is probably true” or “it is often the case. It also separates
“confidence for” from “confidence against”.
MB(H|E) – The measure of belief in hypothesis H given evidence E.
MD(H|E) – The measure of disbelief of H given E.
Where the belief brings together all the evidence that would lead us to believe in P with some
certainty and the plausibility brings together the evidence that is compatible with P and is not
inconsistent with it.
Rules of the algebra:
CF(P1 & P2) = Min(CF(P1),CF(P2))
CF(P1 OR P2) = Max(CF(P1),CF(P2))
Given: IF P THEN Q with CF(R)

CF(Q)=CF(P) * CF(R)
If two rules R1 and R2 support Q with CF(QR1) and CF(QR2) then to find the actual CF(Q):
If both +ve: CF(Q)=CF(QR1) + CF(QR2) - CF(QR1) * CF(QR2)

If both -ve: CF(Q)=CF(QR1) + CF(QR2) + CF(QR1) * CF(QR2)
If of opposite signs: CF(Q)= (CF(QR1) + CF(QR2))/(1 - Min(|CF(QR1)|, |CF(QR2)|))

Casual Networks

This approach accedes to the kind of descriptions provided by experts (e.g. CASNET, ABEL).
Causal models depict relationships as links between nodes in a graph or a network of nodes. It
is critical to explanatory power. Mostly developed for medical application, these networks
provide multiple levels of detail to link clinical findings to pathophysiological state. They
provide focus mechanisms for diagnostic investigation. It exhibits further information seeking
behavior and provides mechanism for accounting for disease interaction.

Limitations

1. A lot of detail required.

2. Not immediately clear how to choose which level to reason at and how to combine
reasoning at different levels. Not a purely mechanistic approach, still unclear when the
problem space is adequately covered.

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