Computation of Extensions of Seminormal Default Theories

Authors:
Kaile Su;Wei Li
Affiliations:
(Correspd.) Institute of Logic and Cognition, Department of Computer Science, Zhongshan University. Guangzhou, 510275, P.R. China. isskls@zsu.edu.cn;(Correspd.) Department of Computer Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing, 100080, P.R. China. liwei@sun670.sebuaa.ac.cn
Venue:
Fundamenta Informaticae
Year:
1999

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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.