The ability of discarding or hiding irrelevant information has been recognized as an important feature for knowledge based systems, including answer set programming. The notion of strong equivalence in answer set programming plays an important role for different problems as it gives rise to a substitution principle and amounts to knowledge equivalence of logic programs. In this paper, we uniformly propose a semantic knowledge forgetting, called HT- and FLP-forgetting, for logic programs under stable model and FLP-stable model semantics, respectively. Our proposed knowledge forgetting discards exactly the knowledge of a logic program which is relevant to forgotten variables. Thus it preserves strong equivalence in the sense that strongly equivalent logic programs will remain strongly equivalent after forgetting the same variables. We show that this semantic forgetting result is always expressible; and we prove a representation theorem stating that the HT- and FLP-forgetting can be precisely characterized by Zhang-Zhou's four forgetting postulates under the HT- and FLP-model semantics, respectively. We also reveal underlying connections between the proposed forgetting and the forgetting of propositional logic, and provide complexity results for decision problems in relation to the forgetting. An application of the proposed forgetting is also considered in a conflict solving scenario.

Logic programs with abstract constraint atoms proposed by Marek and Truszczynski are very general logic programs.They are general enough to captureaggregate logic programs as well asrecently proposed description logic programs.In this paper, we propose a well-founded semantics for basic logic programs with arbitrary abstract constraint atoms, which are sets of rules whose heads have exactly one atom. Weshow that similar to the well-founded semanticsof normal logic programs, it has many desirable properties such as that it can becomputed in polynomial time, and is always correct with respect to theanswer set semantics. This paves the way for using our well-founded semanticsto simplify these logic programs. We also show how our semantics can be applied toaggregate logic programs and description logic programs, and compare itto the well-founded semantics already proposed for these logic programs.

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.