On the consistency of rule bases based on lattice-valued first-order logic LF(X)

The consistency of a rule base is an essential issue for rule-based intelligent information processing. Due to the uncertainty inevitably included in the rule base, it is necessary to verify the consistency of the rule base while investigating, designing, and applying a rule-based intelligent system. In the framework of the lattice-valued first-order logic system LF(X), which attempts to handle fuzziness and incomparability, this article focuses on how to verify and increase the consistency degree of the rule base in the intelligent information processing system. First, the representations of eight kinds of rule bases in LF(X) as the generalized clause set forms based on these rule bases' nonredundant generalized Skolem standard forms are presented. Then an a-automated reasoning algorithm in LF(X), also used as an automated simplification algorithm, is proposed. Furthermore, the a-consistency and the a-simplification theories of the rule base in LF(X) are formulated, and especially the coherence between these two theories is proved. Therefore, the verification of the a-consistency of the rule base, often an infinity problem that is difficult to solve, can be transformed into a finite and achievable a-simplification problem. Finally, an a-simplification stepwise search algorithm for verifying the consistency of the rule base as well as a kind of filtering algorithm for increasing the consistency level of the rule base are proposed. (c) 2006 Wiley Periodicals, Inc.