A3 circuit consistency
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c3martin Offline
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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?
2016-03-29 01:08
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c3martin Offline
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Post: #2
RE: A3 circuit consistency
(2016-03-29 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.
2016-03-29 01:52
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steven Offline
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Post: #3
RE: A3 circuit consistency
Abductive and consistency-based 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.

(2016-03-29 01:52)c3martin Wrote:  
(2016-03-29 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.
2016-03-30 12:27
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