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2.1.1. Redundancy

A knowledge base contains redundancy if there are expressions within it that are not necessary to the inferring of any conclusion by the expert system. Four trivial cases of redundancy can be identified:

Unfireable rule. For example, a rule l —> m would be unfireable if the system
has no way of establishing l, because l is not an input of any rule of the form ... —> l. This anomaly would indicate the need of additional knowledge to obtain l. Another example of unfireable rule is
Duplicate rules. An example of duplicate rules is the following: l1 [wedge] l2 —> m and l2 [wedge] l1 —> m.
Subsumed rule. An example is the following: l1 [wedge] l2 —> m and l1 —> m.
Redundant rule. An example of the general case of redundant rule is the
following: l —> m, m —> n and l —> n. The last rule is redundant, since it can be inferred from the first two rules.

Although redundancy does not indicate real error, it may affect the functioning of the expert system; for instance, if there are redundant rules and if modifications are made to one of the duplicate rules, the other will remain unchanged and thus incorrect. In other words, system builders need to be taken into consideration in redundancy.

2.1.2. Ambivalence

A knowledge is ambivalent if it is possible to infer mutually incompatible conclusions from some set of inputs. Ambivalence anomalies often indicate potentially serious errors. Two cases of ambivalence can be identified:

  1. Conflicting rules. For example, if the knowledge base contains the rules: l1 [wedge] l2 —> m and l1 —> [logical not] m, then at least one of the rules must be incorrect in some way. Additional knowledge may be required to solve the conflicting situation.
  2. Ambivalent rules. For example, if the knowledge base contains the rules: l —> m, m —> n, and l —> [logical not] n.

2.1.3. Circularity

A knowledge base contains circularity if it is possible to enter an endless loop while following some chain of inference. This anomaly could be fatal at run-time if the inference engine does not check for circularity when it tries to fire rules, resulting in an endless loop. An example is the following: l —> m, m —> n and n —> l. If the inference engine can detect and abort loops, then these kinds of anomalies do not have any ill effects.

2.1.4. Deficiency

A knowledge base is deficient if there is some set of inputs for which it will infer no conclusion. Two cases can be identified:

  • Unused input. For example, if l is declared to be an input but there is no rule of the form ... [wedge] l [wedge] ... —> ..., then l is an unused input.
  • Missing rule. The example above suggests that the rule that is supposed to use the data item is missing.

The more general case of deficiency is where there is some logical combination of data items and their values, which, if fed to the knowledge base as input, will not result in any conclusion from the system. This case may suggest that additional knowledge is needed in order to correct the deficiency.


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