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 the rule-based intelligent information processing. In the framework of the lattice-valued first-order logic system LF(X) which is in the attempt of handling fuzziness and incomparability, this paper focuses on how to verify and increase the consistency degree of the rule-base in the intelligent information process system. Firstly, the representations of eight kinds of the rule-bases in LF(X) as the generalized clause set forms based on these rule-bases’ non-redundant generalized Skolem standard forms are presented. Then an -automated reasoning algorithm in LF(X), also used as an automated simplification algorithm, is proposed. Furthermore, the -consistency and the -simplification theories of the rule-base in LF(X) are formulated, especially the coherence between these two theories is proved. Therefore, the verification of the -consistency of the rule-base, often an infinity problem which is difficult to be achieved, can be transformed into a finite and achievable -simplification problem. Finally, an -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.