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2. THEORETICAL FOUNDATION OF EXPERT SYSTEM VERIFICATION AND VALIDATIONIn general, V & V of expert systems consists of identifying anomalies such as redundant, contradictory, or deficient knowledge. An anomaly is a difference between what is expected of KB structure and system performance, and what is actually observed. Anomalies are considered as potential errors since not all of them are errors. However, many common KB errors can be identified by identifying anomalies. Anomalies may also result in inefficiency in terms of performance, maintenance, etc. Before commencing the discussion on the theoretical foundation of expert system V&V, a short note on representations is needed. Most of the work concerning the errors and anomalies that can occur in expert systems has been carried out on rule-based representations. Parallels do exist with frame- and object-based representations. In this section we concentrate on two principal methods of knowledge representation used in expert systems: production rules and object-based representations. Since both rule-based and structured object representational paradigms have their strengths, some efforts have been made to combine the two. 2.1. LOGICAL FOUNDATION OF RULE-BASED ANOMALIESA variety of methods have been built for detecting the above-mentioned anomalies in rule bases. The early methods looked for anomalies between pairs of rules only, while the most sophisticated methods detect anomalies manifested over chains of inference. Rule-based expert systems have foundation in formal logic. There is a relation between the production rules of such systems and the implication statements of logical theorems, and also between the facts of the knowledge base and the axioms of logic. This relationship has been the basis for systematic checking methods for rule bases. These methods can be used to determine the internal self-consistency and completeness of rule bases, by interpreting the rules as logical expression followed by syntactic inspection and manipulation. However, terms such as consistency and completeness have slightly different meanings, as shown in Table 1.
We choose to focus upon rule-based expert systems that are based on first-order logic because rule-based systems are the most widely used type of expert system and the semantics of rule-based systems based on logic are well known. The theoretical framework in which anomaly detection systems for rule-based knowledge bases have been be analyzed is based on the first-order logic. The terminology and notation used to express the knowledge base is the following (Preece and Shinghal, 1994):
The anomalies of rule bases can be informally defined as follows:
The use of formal logic will enable us to detect each type of anomaly by considering only the syntactic form of expressions in the knowledge base. For example, consider the two rules l1 [wedge] l2 > m and l1 > m. From an understanding of the semantics of the logical operators [wedge] ("and") and > ("implies"), the first rule is redundant, since it is just a specific version of the second one, which is more general. We can detect this by looking for that particular case of redundancy in which we have two rules with identical consequences, such that the literals in the antecedent of one rule are a subset of the literals in the antecedent of the other. It is important to realize that such anomalies may not represent actual errors in a rule base, but rather symptoms of possible errors. For example, a redundant rule may occur because there is missing knowledge, the rule l1 > m should have been l1 [wedge] l3 > m. It is up to the knowledge engineer together with the human expert to decide what actions to take when such anomalies are detected. Based on the semantics of first-order logic, four basic types of anomaly have been identified by Preece et al. (1992), some of which have a number of special cases as shown in Figure 1.
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