CERTAINTY FACTOR EXAMPLE

Let’s consider a concrete example (of a home-lawn) in which:

S: sprinkler was left on last night

W: grass is wet in the morning

R: it rained last night

We can write MYCIN-style rules which describe predictive relationships among these three events:

R1: If the sprinkler was left on last night

then there is suggestive evidence (0.9) that

the grass will be wet this morning

Taken alone, R1 may accurately describe the world. But now consider a second rule:

R2: If the grass is wet this morning

then there is suggestive evidence (0.8) that it rained last right

Taken alone, R2 makes sense when rain is the most common source of water on the grass. But, if the two rules, are applied together, using MYCIN’s rule for chaining,

we get

MB [W, S] = 0.8 [sprinkler suggests wet)

MB [R, W] = 0.8. 0.9 = 0.72 [wet suggests rains]

In other words, we believe that it rained because we believe the sprinkler was left on. We get this despite the fact that if the sprinkler is known to have been left on and to be the cause of the grass being wet, then there is actually almost no evidence for rain (because the wet grass has been explained due to sprinkler).

One of the major advantages of the modularity of the MYCIN rule system is that it allows us to consider individual antecedent/consequent relationships independently of others. In particular, it lets us talk about the implications of a proposition without going back and considering the evidence that supported it.

Unfortunately, this example shows that there is a danger in this approach whenever the justifications of a belief are important to determining its consequences. In this case, we need to know why we believe the grass is wet (because we observed it to be wet as opposed to because we know the sprinkler was on) in order to determine whether the wet grass is evidence for it having just rained.

A word of caution; this example illustrates a specific rule structure which almost always causes trouble and should be avoided. Our rule R, describes a causal relationship between wetness and sprinkler (sprinkler causes wet grass). The rule R1 although, looks the same, actually describes an inverse causality relationship (wet grass is caused by rain and thus is evidence for its cause).

We can form a chain of evidence from cause of an event:

But the evidence should not be used to look for the cause or symptom of an event without any new information. To avoid this problem, many rule-based systems either limit their rules to one structure or clearly partition the two kinds so that they cannot interfere with each other. The Bayesian network suggest a systematic solution to this problem.

We can summarise this discussion of certainty factors and rule-based systems which is very useful but will be appreciated only after you are done with the expert systems. The approach makes strong independence assumptions which make it relatively easy to use; at the same time assumptions create dangers if rules are not written carefully so that important dependencies are captured.

The approach can serve as the basis of practical application programs. It did so in MYCIN. It has also done so in a broad array of other systems which have been built in the EMYCIN platform, which is a generalisation (often called a shell) of MYCIN with all the domain-specific knowledge expressed, rules stripped out. One reason that this framework is useful, despite its limitations, is that it appears that in an otherwise robust system the exact numbers which are used do not matter very much.

The other reason is that the rules were carefully designed to avoid the major pitfalls we have just described. One other interesting thing about this approach is that it appears to mimic quite well the way people manipulate certainties.