arXiv:2505.06505cs.AI2025-05IJCAI被引 1

用偏好关系定义信念代数,实现确定性迭代信念更新。

On Definite Iterated Belief Revision with Belief Algebras

  • 以信念代数表示信念与新证据,通过偏好关系建模
  • 引入上界约束后,每次更新结果唯一确定
  • 适合安全关键场景,支持可预测的信念演化

传统基于逻辑的信念修正研究聚焦于设计约束修正算子行为的规则。尽管已有框架用于刻画迭代修正规则,但通常过于宽松,导致在相同信念条件下存在多个满足规则的修正算子。在许多实际应用(如安全关键系统)中,需要指定一个确定的修正算子,使智能体能够以确定性方式迭代修正信念。本文提出一种新型迭代信念修正框架,通过偏好关系刻画信念信息。语义上,信念与新证据均表示为信念代数,为信念修正提供丰富且表达力强的基础。在传统修正规则基础上,引入信念代数修正的额外公理,包括对修正结果的上界约束。我们证明:在给定当前信念状态和新证据时,修正结果是唯一确定的。为进一步提升实用性,我们设计了一种具体算法来执行该修正过程。我们认为,该方法可提供更可预测、更原则性的信念修正机制,适用于真实世界应用。

原文摘要 · Abstract (English)

Traditional logic-based belief revision research focuses on designing rules to constrain the behavior of revision operators. Frameworks have been proposed to characterize iterated revision rules, but they are often too loose, leading to multiple revision operators that all satisfy the rules under the same belief condition. In many practical applications, such as safety critical ones, it is important to specify a definite revision operator to enable agents to iteratively revise their beliefs in a deterministic way. In this paper, we propose a novel framework for iterated belief revision by characterizing belief information through preference relations. Semantically, both beliefs and new evidence are represented as belief algebras, which provide a rich and expressive foundation for belief revision. Building on traditional revision rules, we introduce additional postulates for revision with belief algebra, including an upper-bound constraint on the outcomes of revision. We prove that the revision result is uniquely determined given the current belief state and new evidence. Furthermore, to make the framework more useful in practice, we develop a particular algorithm for performing the proposed revision process. We argue that this approach may offer a more predictable and principled method for belief revision, making it suitable for real-world applications.

信念修正逻辑推理形式化方法

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