Using Petri Nets for Error Detecting and Uncertainty Reasoning of Rule Base Systems

• Main Author: 鄭成斌
• Other Authors: Stephen J.H. Yang
• Format: Others
• Language: zh-TW
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/10689757377870515261

碩士 === 國立中央大學 === 資訊工程研究所 === 87 === An expert system is a computer system with knowledge (facts, rules, and inference mechanism) of domain experts. The heart of an expert system is the rule base, which consists of the facts and rules acquired from the domain experts. Users of an expert system can interact with the system with queries as the same way that they consult with the domain experts for obtaining knowledge. In general, the procedures for domain experts to accumulate knowledge and expertise are incremental and intuitive, thus, a rule base need to be constructed incrementally and experienced multiple times of refinement. Besides, an expert system is usually constructed by consulting with numerous experts, and experts may have conflict expertise. Therefore, it is not surprised that many rules in a rule base may have structural errors. As addressed in [suwa82, naza89, nguy87, rama97, zhan94], structural errors can be classified as redundancy (due to redundant rules, subsumed rules); inconsistency (due to conflict rules); incompleteness (due to missing rules), and circularity (due to infinite inference). The set of rules involved in any structural errors can be a pair of rules or a chain of rules. Fuzzy set theory [zade65, zade88] has been used as a formal framework for representing and reasoning real-world information which in general are characterized with imprecision, vagueness, approximation, and uncertainty. One of the successful applications of fuzzy set theory is the fuzzy control system whose applications can be found in areas such as consumer electronics, flexible manufacturing systems, auto industry, and many other complex systems [muna94]. In general, fuzzy control systems can be implemented as rule-based systems with certainty factors, while these systems can be viewed as a result of fuzzifying rule-based systems [muna94, zade92]. One important capability of rule-based system with certainty factors is to answer questions with imprecise and incomplete information while the answers may be revised at later time if more complete and precise information is available. Compared with conventional rule-based systems, the inference mechanism of rules with certainty factors characterized themselves in two perspectives: simplicity and humanity. Fuzziness captures the approximate and inexact nature of the real world that is more like the intuitive way of human thinking. We are presenting a mechanism based on Petri nets for uncertainty reasoning rule-based systems with imprecise information in the problem domain of resolution rules. We use the high-level Petri nets model to describe the behavior of rule inference. There are two parts to our approach. One is to establish a sound rule-based system, and the other is to add certainty factor into the system for rule inference. This mechanism provides for normalizing rules with certainty factor of a rule-based system, transforming the rules into a high-level Petri net, verifying a Petri nets formalism of rule-based systems, and answering queries based on the net with imprecise information, respectively. A rule-based system is often build in an incremental, piecemeal fashion, and potential errors may be inadvertently brought into it. At the first parts, our verification is based on Petri nets and their incidence matrix, so we can use methods of analysis for Petri nets. We have developed a tool consisting of the following three phases: rule normalization, rules to high-level Petri net transformation, and rule verification. In phase one, we normalize the rules into Horn clauses, then transform the rules into a Petri net and its corresponding incidence matrix in phase two. In phase three, we perform the rule verification based on the incidence matrix. At the second part, the values of truth degree are added into high-level Petri nets and are computed in algebraic form based on the state equation, which can be implemented in matrix computation in Petri nets.