A3 circuit consistency

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c3martin
Student
Reputation: 0

A3 circuit consistency
I tried figuring out how they got some configurations of Ab(x) predicates to be consistent or not, but I couldn't.
If there isn't a specified functionality for abnormal AND gates then their outputs are unknown right?
Therefore, how is the circuit is consistent if Ab(a1) and Ab(o1) (regardless of the others) since both their outputs are undefined?


20160329 01:08 

c3martin
Student
Reputation: 0

RE: A3 circuit consistency
(20160329 01:08)c3martin Wrote: I tried figuring out how they got some configurations of Ab(x) predicates to be consistent or not, but I couldn't.
If there isn't a specified functionality for abnormal AND gates then their outputs are unknown right?
Therefore, how is the circuit is consistent if Ab(a1) and Ab(o1) (regardless of the others) since both their outputs are undefined?
I figured it out.
The observed outputs are not the ones that a normal full adder would give. Thus, when all the gates are normal, the results are not entailed. Also, they're inconsistent because it does output something, which means that the circuit is apparently okay, when it is clearly not.


20160329 01:52 

steven
Instructor
Reputation: 0

RE: A3 circuit consistency
Abductive and consistencybased diagnosis are explained on pages 275 and 277 of the textbook, respectively. For abductive diagnosis: "What we are looking for, roughly is a minimal conjunction alpha of ground Ab(t) and ~Ab(t) terms such that
KB U Settings U {alpha} = Observations.
For consistency based diagnosis: "We want to find a set of components D such that the set
{Ab(t)  t \in D} U {~Ab(t)  t \not \in D}
is consistent with the set
KB U Settings U Observations
and no proper subset of D is.
You are given a fault model for the AND gates. For the NOT and OR gates, if the gate is faulty, the output of the gate is unknown.
(20160329 01:52)c3martin Wrote: (20160329 01:08)c3martin Wrote: I tried figuring out how they got some configurations of Ab(x) predicates to be consistent or not, but I couldn't.
If there isn't a specified functionality for abnormal AND gates then their outputs are unknown right?
Therefore, how is the circuit is consistent if Ab(a1) and Ab(o1) (regardless of the others) since both their outputs are undefined?
I figured it out.
The observed outputs are not the ones that a normal full adder would give. Thus, when all the gates are normal, the results are not entailed. Also, they're inconsistent because it does output something, which means that the circuit is apparently okay, when it is clearly not.


20160330 12:27 

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