Affiliations: Institute of Logic and Cognition, Department of Computer Science, Zhongshan University. Guangzhou, 510275, P.R. China. [email protected] | Department of Computer Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing, 100080, P.R. China. [email protected]
Note: [] Address for correspondence: Department of Computer Science, Zhongshan University, Guangzhou, 510275, P.R. China
Note: [] Address for correspondence: Department of Computer Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing, 100080, P.R. China
Abstract: In Reiter's default logic, the operator in the fixed-point definition of extension is not appropriate to compute extensions by its iterated applications. This paper presents a class of alternative operators, called compatible ones, such that, at least for normal default theories and so-called well-founded, ordered default theories, we can get extensions by iterated applications of them. In addition, we completely answer Etherington's conjectures about both his procedure for generating extensions and a modified version of it. In particular, we give an example of a finite, ordered default theory, for which the original procedure fails to converge, and show that the computation of the modified one is essentially the iteration of a compatible operator and converges for finite, ordered theories.
