Forgetting is an important concept in knowledge representation and automated reasoning with widespread applications across a number of disciplines. A standard forgetting operator, characterized in [26] in terms of model-theoretic semantics and primarily focusing on the propositional case, opened up a new research subarea. In this paper, a new operator called weak forgetting, dual to standard forgetting, is introduced and both together are shown to offer a new more uniform perspective on forgetting operators in general. Both the weak and standard forgetting operators are characterized in terms of entailment and inference, rather than a model theoretic semantics. This naturally leads to a useful algorithmic perspective based on quantifier elimination and the use of Ackermann's Lemma and its fixpoint generalization. The strong formal relationship between standard forgetting and strongest necessary conditions and weak forgetting and weakest sufficient conditions is also characterized quite naturally through the entailment-based, inferential perspective used. The framework used to characterize the dual forgetting operators is also generalized to the first-order case and includes useful algorithms for computing first-order forgetting operators in special cases. Practical examples are also included to show the importance of both weak and standard forgetting in modeling and representation.

遗忘是知识表示和自动推理中的一个重要概念，在多个学科中广泛应用。一个标准的遗忘算子，在[26]中以模型理论语义为特征，主要关注命题案例，开辟了一个新的研究领域。在本文中，介绍了一种称为弱遗忘的新算子，它与标准遗忘是双重的，并且两者一起为一般的遗忘算子提供了一个新的更统一的视角。弱遗忘算子和标准遗忘算子的特征都是蕴涵和推理，而不是模型理论语义。这自然会带来基于量词消除和阿克曼引理及其不动点泛化的使用的有用算法视角。标准遗忘与最强必要条件和弱遗忘与最弱充分条件之间的强形式关系也可以通过使用基于蕴涵的推理视角来很自然地表征。用于表征对偶遗忘算子的框架也被推广到一阶情况，并包括在特殊情况下计算一阶遗忘算子的有用算法。还包括实际例子来展示弱遗忘和标准遗忘在建模和表示中的重要性。