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Next: 6.3 Alternatives for Critique Up: 6 A Scenario of Previous: 6.1 The Input-problem

6.2 The steps in the PCM method


We have to propose a method with definitions for each of the six components. The goal that guides the choice for the Cover and NotContra components is explanation-notion(standard), since the system contains knowledge that standard entailment is most frequently used in diagnostic methods (as opposed to the use of non-standard variatons of entailment proposed in [ten Teije & van Harmelen, 1996a]). As a result, we choose for both explanation relations ( Cover and NotContra) the classical entailment relations ( and respectively). The other four components are chosen blindly.

The proposed method isgif:


In Table 7 the definitions of the components are briefly described. In [ten Teije & van Harmelen, 1994] the definitions of some of these components are given more formally.

Figure 7: The components of the proposed method.

The dynamic goals now become all the goals that have not already been statically determined. In this case the only dynamic goal is max-number-diagnoses(2).


One of the usual constraints on diagnostic methods is to demand that the Cover component is at least as strong as the NotContra component. After all, if an observable is entailed by a consistent theory, then that observable is also consistent with this theory.

The method described by term (3) does not violate this constraint. However, there is another assumption conflict, because #-min assumes that every cause has equal likelyhood. This means that the knowledge-verification step has failed, and therefore a new propose step is started.


We now propose another method. Because this step is still guided by the same static goal as before ( explanation-notion(standard)), the method still contains as Cover definition and as NotContra definition. The other components are again chosen blindly. The propose method is nowgif:



As in `` knowledge-verification'' there is no violation of the constraint concering the Cover and NotContra components. The other assumption-confllict also disappears because does not assume equal likelyhood of causes. As a result, in this case assumptions conflicts no longer occur.


In this step the system performs diagnosis using the valid method of term (4). Based on the computed diagnoses it tests the dynamic goals.

Using the method of the term (4) results in the following and . The vocabulary defined by initial-fault-nodes contains all the initial nodes of Figure 6 that correspond to fault-modes, plus all the assumption-symbols . Performing diagnosis results in ``no diagnosis'', which becomes the verification result.


The reason for not finding any diagnoses is that there is no explanation for lights(yes): only incompleteness assumptions ('s) and faults are part of the vocabulary ( initial-fault-nodes), and a fault cannot explain the correct behaviour of lights(yes) when we use and for Cover and NotContra respectively. This step determines that a possible suitable repair action is adapting the Obs-mapping. This is so because a different Obs-mapping might require only incorrect behaviour to be explained (as apposed to all behaviour, including correct behaviour, as is the case withe the current definition, namely Obs-mapping=abd-mapping).


The modify step must now repair the component specified by the critique step. The repair action is determined by first generating a set of variants of the Obs-mapping, and then applying two filters on this generated set of Obs-mapping definitions.

generate: generate variants of the Obs-mapping component.

We require that any solution of the method using the original Obs-mapping is also a solution for the adapted method with the new Obs-mapping (after all, we want to increase the set of solutions). This relation is expressed in the predicate subset-Es(Old,New). It denotes that the explanations generated by a method with Obs-mapping-component Old are also generated by a method with Obs-mapping-component New, provided all the other components remain the same. In this generation step we generate those Obs-mapping definitions which satisfy subset-Es(abd-mapping,New):

For our problem, the system generates the following set based on its factual knowledge of subset-Es:


The complete definitions of these Obs-mapping components are in [ten Teije & van Harmelen, 1994], but in sloppy notation these definitions are given in table 8.

Figure 8: denotes the possible observable values, and OBS denotes the currently given observations

The generated set of Obs-mapping definitions is now:


because subset-Es(abd-mapping,New) holds for these elements.

: of all the possible candidate repairs, we prefer the variants that are the ``closest'' to the original Obs-mapping component:

We define ``closest'' as those Obs-mapping definitions whose set is (1) in any case no superset of the original set (since we do not want to explain more observable values strongly) and (2) is not a subset of another possible set (since we want to delete as few observable values as possible).

The predicate closest-Obs-mapping is therefore defined as follows, whereby denotes that the Obs-mapping X gives an set that is a subset of the set computed by the Obs-mapping Y.

We filter the set based on the following factual knowledge of :

This factual knowledge, just as the knowledge in (5), is stored as given facts in our system. However, given sufficiently powerful theorem-proving techniques, it would be possible for the system to automatically derive these facts from the definitions in table 8. From these definitions, it follows that closest-Obs-mapping holds for the Obs-mapping definitions polarity-mapping and abnormality-mapping. The FilteredSet is therefore:


: We now filter those variants which result in the same solutions as the original method in the current case. In this filter the system executes a part of the diagnosis, namely the Obs-mapping definition. The results of the possible Obs-mapping definitions have to be computed and compared with the outputs of the original Obs-mapping. Those which give the same and will be deleted from the set. In contrast with , this filter is specific for the current problem on hand, whereas the was independent of the problem.

Applying the Obs-mapping definitions from (6) to OBS={light(yes),engine-starting(no)} gives the following values for and :


We see that the Obs-mapping with value polarity-mapping gives the same sets as the original Obs-mapping (which had value abd-mapping). The Obs-mapping with value abnormality-mapping gives other sets. This results in a FilteredSet where the only Obs-mapping is abnormality-mapping.

The modify therefore results in the method:


The originally proposed method of term (4) could not handle observed behaviour that was correct behaviour. The above critique-&-modify step tried to recover from this shortcoming by adapting the Obs-mapping component, resulting in the method from term (11). The next step is to verify the adapted method.


The knowledge verification still succeeds, since the Cover-, NotContra- and Selection-components and the assumptions have not changed. (see `` Knowledge-verification'')


Again we perform diagnosis, but now using the modified method of term (11). Performing diagnosis results in the following diagnoses:


Unfortunately, the test whether the dynamic goal max-number-diagnoses(2) is satisfied fails. This means we have to perform another critique step.


In the verification step the problem of too many solutions was recognized. A repair action for this problem is a modification of the Selection component. If the new Selection component is a stronger filter, then less diagnoses will be left. The system uses the knowledge that constructing the conjunction of the current Selection-component with an additional selection criterion will have this effect.


The repair action of configuring the new Selection criterion is executed in this step. In our case the Vocabulary ( initial-fault-nodes) contains faults and incompleteness-assumptions. We can therefore eomply a selection-criterial that prefers explanations which are subset-minimal in the incompleteness assumptions (). The proposed Selection criterion then becomes `` and ''.

The adapted method is:


The proposed method from (11) resulted in too many diagnoses. The above critique and modify steps tried to recover from ``too many diagnosis'' and have modified the method. This modified method now has to be verified.


The knowledge verification still satisfies, as before ( also does not violate the unequal-likelyhood assumption).


Again we perform diagnosis using the modified method of term (9). Performing diagnosis results in the following diagnosis:


Checking this against the dynamic goal shows that we have now also satisfied max-number-diagnoses(2).

We have now (finally!) solved the original diagnostic problem specified in (2). The method of term (9) has explained the observations {engine-starting(no),lights(yes)} under the assumption ``the causes are different in likelyhood'' for the desired goals ``use a standard notion of explanation'' and ``at most two alternative diagnoses are allowed''. The sole computed diagnosis is (14).

During this diagnostic problem solving process the configuration system has had to recover from the initial inability to deal with correct behaviour (by modifing the Obs-mapping component) and it had to recover from ``too many solutions'' caused by too weak a selection filter (by modifying the Selection component).

next up previous
Next: 6.3 Alternatives for Critique Up: 6 A Scenario of Previous: 6.1 The Input-problem

Frank van Harmelen
Fri Oct 4 13:40:35 MET DST 1996