Differently implicational α-universal triple I restriction method of (1, 2, 2) type

From the viewpoints of both fuzzy system and fuzzy reasoning, a new fuzzy reasoning method which contains the α- triple I restriction method as its particular case is proposed. The previous α-triple I restriction principles are improved, and then the optimal restriction solutions of this new method are achieved, especially for seven familiar implications. As its special case, the corresponding results of α-triple I restriction method are obtained and improved. Lastly, it is found by examples that this new method is more reasonable than the α-triple I restriction method.

Mathematical Foundation of Basic Algorithms of Fuzzy Reasoning

Algorithm of fuzzy reasoning has been successful applied in fuzzy control,but its theoretical foundation of algorithms has not been thoroughly investigated. In this paper,structure of basic algorithms of fuzzy reasoning was studied, its rationality was discussed from the viewpoint of logic and mathematics, and three theorems were proved. These theorems shows that there always exists a mathe-~matical relation (that is, a bounded real function) between the premises and the conclusion for fuzzy reasoning, and in fact various algorithms of fuzzy reasoning are specific forms of this function. Thus these results show that algorithms of fuzzy reasoning are theoretically reliable.

Functional Dependencies and Its Axiom System in XML

According to the analysis of existing complicated functional dependencies constraint, we conclude the conditions of defining functional dependency in XML, and then we introduce the concept of the node value equality. A new path language and a new definition of functional dependencies in XML （XFD） are proposed XFD includes the relative XFD and the absolute XFD, in which absolute key and relative key are the particular cases. We focus on the logical implication and the closure problems, and propose a group of inference rules. Finally, some proofs of the correctness and completeness are given. XFD is powerful on expressing functional dependencies in XML causing data redundancy, and has a complete axiom system.

On the inference rules in legal logic

Inference rules are at the heart of studies of logic. Although legal logic is an applied logic, it is not a simple application of the inference rules of formal logic in the legal domain, but the outcome of a combination of the inference rules of formal logic and inference rules peculiar to the legal domain. Therefore, although legal inference rules have some features in common with the inference rules of formal logic, they also have a distinctive character. Their common features are to be found in the fact that the basic inference rules of formal logic are an indispensable part of the inference rules of legal logic, while their distinctiveness lies in the fact that legal inference rules contain a special inference rule that does not exist in formal logic, the rule of burden of proof.

A NEW EVIDENCE UPDATING RULE BASED ON CONDITIONAL EVENT

Updating or conditioning a body of evidence modeled within the DS framework plays an important role in most of Artificial Intelligence (AI) applications. Rule is one of the most important methods to represent knowledge in AI. The appearance of uncertain reasoning urges us to measure the belief of rule. Now,most of uncertain reasoning models represent the belief of rule by conditional probability. However,it has many limitations when standard conditional probability is used to measure the belief of expert system rule. In this paper,AI rule is modelled by conditional event and the belief of rule is measured by conditional event probability,then we use random conditional event to construct a new evidence updating method. It can overcome the drawback of the existed methods that the forms of focal sets influence updating result. Some examples are given to illustrate the effectiveness of the proposed method.

An Operational Approach to Belief Revision

A deduction system, called RE-proof system, is constructed for generating the revisions of first order belief sets. When a belief set is rejected by a given fact, all maximal subsets of the belief set consistent with the fact can be deduced from the proof system. The soundness and completeness of the RE-proof system are proved, which imply that there exists a resolution method to decide whether a revision retains a mtalmal subset of a belief set.