Forgetting Revisited

In this paper, we propose an alternative notion, called weak forgetting, of forgetting a set of predicates in a first-order theory. One important feature of this new notion is that the result of weak forgetting is always first-order expressible. In contrast, this is not the case for the traditional notion of forgetting, called strong forgetting, introduced by Lin and Reiter. As a consequence, these two notions are not exactly the same. Interestingly, we prove that they coincide when the result of strong forgetting is first-order expressible. We also present a representation theorem to characterize weak forgetting from different aspects.

Authors

• Yi Zhou Southeast University Key Laboratory of New Generation Artificial Intelligence Technology and Its Interdisciplinary Applications, Ministry of Education, China
• Yan Zhang School of Computer Science, Hubei University

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