Common Sense Reasoning in Diagnostic Systems - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 112

<O4=1, {{Inv1,Inv4}}>;
<O3=1, {{And2}}>;
<O3=0, {{Inv3}}>;
<O2=0, {{And2,Inv5}}>;
<O2=1, {{Inv2}, {And4,Inv1,Inv3,Inv4,Inv5,Inv6}}>;
<O1=1, {{And2}}>;
<O1=0, {{Inv1}}>.

Fig. 9. The 3-bit parity checker

As we are interested with a measurement point with the greatest information on failure the
point is selected from a quantity of assumptions.
Designate an environment set as Envs ( x ). So, for the considered example,
Envs ( O1 )={{And2}, {Inv1}}. Let's introduce the function Quan ( x ), by which we will designate
the information quantity obtained at measuring values in the point x .
If the environment J represents a unique assumption, then obviously the set
cardinality will be equal 1: | J | = 1. The information quantity obtained from such
environment is equal to 1. If the environment consists more than one component the
information quantity obtained at confirming or refuting a value is less because we have
knowledge not about a concrete valid / fault component but about a component set among
of which are faulty. Therefore the information quantity obtained from an environment
consisting of more than one assumption, we heuristically accept equal to half of set
cardinality. Thus the function Quan ( x ) is:

| | J

 

j

Quan x ()  | | J 

(1)

i

2

J  Envs x () J  Envs x () i j

||1 J 

||1 J 

i

j