arXiv:2507.02319cs.AIcs.LO2025-07

提出信念修正的可达成能力框架,揭示不同修正机制的内在潜力。

Iterated belief revision: from postulates to abilities

  • 从公理转向能力分析,关注信念能否达到特定状态
  • 证明多种修正机制具备塑性、等价、教条等不同能力
  • 适合研究信念演化与逻辑系统设计的学者

信念修正领域虽新提案众多,但对现有方法的分析却十分匮乏。多数工作依赖公理作为语法刻画:某种修正机制等价于某些性质。公理仅约束特定修正实例必须如何更新信念,却忽略其能实现何种状态。例如,能否达到任意信念状态?能否从无初始信念出发达成所有可能状态?能否形成教条式信念(即未被相信的皆不可能)?能否使两个条件同等被相信?若应用场景中所有信念状态均合理,则需确保每种状态均可达;若需等价信念,则该状态也须可达;若允许教条信念,则需具备生成该状态的能力。这些是能力问题,而非公理所规定的约束。本文系统分析了多种信念修正机制(如词典序、自然、受限、极端、全交集、剧烈、严重、中度严重、深度严重、普通严重及深度严重修正)所具备的可达成能力,包括塑性、等价性、教条性、遗忘、纠正、皈依、可学习等,揭示了各类机制在实现特定信念状态方面的优势与局限。

原文摘要 · Abstract (English)

The belief revision field is opulent in new proposals and indigent in analyses of existing approaches. Much work hinge on postulates, employed as syntactic characterizations: some revision mechanism is equivalent to some properties. Postulates constraint specific revision instances: certain revisions update certain beliefs in a certain way. As an example, if the revision is consistent with the current beliefs, it is incorporated with no other change. A postulate like this tells what revisions must do and neglect what they can do. Can they reach a certain state of beliefs? Can they reach all possible states of beliefs? Can they reach all possible states of beliefs from no previous belief? Can they reach a dogmatic state of beliefs, where everything not believed is impossible? Can they make two conditions equally believed? An application where every possible state of beliefs is sensible requires each state of beliefs to be reachable. An application where conditions may be equally believed requires such a belief state to be reachable. An application where beliefs may become dogmatic requires a way to make them dogmatic. Such doxastic states need to be reached in a way or another. Not in specific way, as dictated by a typical belief revision postulate. This is an ability, not a constraint: the ability of being plastic, equating, dogmatic. Amnesic, correcting, believer, damascan, learnable are other abilities. Each revision mechanism owns some of these abilities and lacks the others: lexicographic, natural, restrained, very radical, full meet, radical, severe, moderate severe, deep severe, plain severe and deep severe revisions, each of these revisions is proved to possess certain abilities.

信念修正逻辑能力认知建模

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