arXiv:2508.21441cs.AI2025-08被引 1

提出一种通用遗忘框架,用排序函数实现知识更新。

A General Framework of Epistemic Forgetting and its Instantiation by Ranking Functions

  • 基于斯波恩排序函数构建五类认知遗忘类型
  • 给出七种具体遗忘操作并系统验证其性质
  • 适合逻辑推理与信念管理研究者参考

遗忘作为一种知识管理操作,主动忽略智能体的部分知识与信念,原因多样。现有研究主要依赖两类算子:一是变量消除,通过剔除原子变量聚焦剩余语言,多用于逻辑程序与答案集编程;二是AGM信念修正中的收缩操作,通过逻辑推导从信念集中移除命题。两者均基于经典逻辑。本文从认知视角出发,研究具有丰富语义结构的信念状态下的遗忘机制,并与命题逻辑建立清晰联系。由此探讨认知背景中遗忘的意义,将已有及新式遗忘操作提升至认知层面。我们提出五类通用认知遗忘形式,并以斯波恩排序函数实例化为七种具体遗忘操作。借鉴逻辑编程与AGM理论的遗忘公理,构建一套完整评价体系。最终对所有具体操作进行全维度评估,揭示不同算子间的异同,形成新颖的综合性分析视角。

原文摘要 · Abstract (English)

Forgetting as a knowledge management operation deliberately ignores parts of the knowledge and beliefs of an agent, for various reasons. Forgetting has many facets, one may want to forget parts of the syntax, a proposition, or a conditional. In the literature, two main operators suitable for performing forgetting have been proposed and investigated in depth: First, variable elimination is a syntactical method that blends out certain atomic variables to focus on the rest of the language. It has been mainly used in the area of logic programming and answer set programming. Second, contraction in AGM belief revision theory effectively removes propositions from belief sets under logical deduction. Both operations rely mainly on classical logics. In this article, we take an epistemic perspective and study forgetting operations in epistemic states with richer semantic structures, but with clear links to propositional logic. This allows us to investigate what forgetting in the epistemic background means, thereby lifting well-known and novel forgetting operations to the epistemic level. We present five general types of epistemic forgetting and instantiate them with seven concrete forgetting operations for Spohn's ranking functions. We take inspiration from postulates of forgetting both from logic programming and AGM theory to propose a rich landscape of axioms for evaluating forgetting operations. Finally, we evaluate all concrete forgetting operations according to all postulates, leading to a novel comprehensive overview highlighting differences and commonalities among the forgetting operators.

认知推理信念更新遗忘机制

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