A Framework of Fuzzy Diagnosis

Fault diagnosis has become an important component in intelligent systems, such as intelligent control systems and intelligent eLearning systems. Reiter's diagnosis theory, described by first-order sentences, has been attracting much attention in this field. However, descriptions and observations of most real-world situations are related to fuzziness because of the incompleteness and the uncertainty of knowledge, e. g., the fault diagnosis of student behaviors in the eLearning processes. In this paper, an extension of Reiter's consistency-based diagnosis methodology, Fuzzy Diagnosis, has been proposed, which is able to deal with incomplete or fuzzy knowledge. A number of important properties of the Fuzzy diagnoses schemes have also been established. The computing of fuzzy diagnoses is mapped to solving a system of inequalities. Some special cases, abstracted from real-world situations, have been discussed. In particular, the fuzzy diagnosis problem, in which fuzzy observations are represented by clause-style fuzzy theories, has been presented and its solving method has also been given. A student fault diagnostic problem abstracted from a simplified real-world eLearning case is described to demonstrate the application of our diagnostic framework

Semantics and Complexity of Abduction from Default Theories

Abductive reasoning (roughly speaking, find an explanation for observations out of hypotheses), has been recognized as an important principle of common-sense reasoning. Since logical knowledge representation is commonly based on nonclassical formalisms like default logic, autoepistemic logic, or circumscription, it is necessary to perform abductive reasoning from theories (i.e. knowledge bases) of nonclassical logics. In this paper, we investigate how abduction can be performed from theories in default logic. In particular, we present a basic model of abduction from default theories. Different modes of abduction are plausible, based on credulous and skeptical default reasoning; they appear useful for different applications such as diagnosis and planning. Moreover, we thoroughly analyze the complexity of the main abductive reasoning tasks, namely finding an explanation, deciding relevance of a hypothesis, and deciding necessity of a hypothesis. These problems are intractable even..