Sequence of knowledge bases and evaluating revision approximately

This paper is motivated to give a recursion-theoretic framework to investigate sequences of knowledge bases such as sequence of iterated revisions and sequence of provisional outputs generated by a so-called anytime algorithm. The global properties of sequence of general knowledge bases are studied by using some concepts such as convergence and logical convergence, which can be considered not only as rationality postulates sequence of iterated revisions but also as basic criteria of adequacy for anytime algorithms for evaluating knowledge bases. A quite surprising result in this paper is that, even in the full first-order logic case, revising a knowledge could be effectively done by an anytime algorithm that produces quickly a first version of the revision and refines it step by step, and these versions approach the revision in limit. It is also investigated that the problem of how to approximately compute an extension in default logic.