arXiv:2508.03465cs.AI2025-08被引 1

用图结构建模信念,区分可信度与信心,揭示认知矛盾。

Toward a Graph-Theoretic Model of Belief: Confidence, Credibility, and Structural Coherence

  • 将信念视为带权重的有向图,节点为信念,边表支持或冲突关系。
  • 引入可信度(来源信任)与信心(内部结构支持)双指标,不依赖概率更新。
  • 适合研究信念系统内部结构、矛盾与认知状态分类,非推理或修正模型。

信念系统常被简化为全局一致的命题集合或标量概率分布,这类表示方式掩盖了信念的内在结构,混淆了外部可信度与内部一致性,并难以建模碎片化或矛盾的认知状态。本文提出一种最小化的信念系统形式化框架:将信念表示为有向加权图,其中节点代表具体信念,边编码认知关系(如支持或矛盾),并引入两个独立函数分别赋予每个信念可信度(反映信息源信任程度)和信心(由内部结构支持决定)。该方法不假设先验一致性,也无需信念更新机制;相较于经典概率模型,避免了对完备性的预设;相较于逻辑或论证框架,能实现更精细的结构表达,且不强制二值化证明状态或演绎封闭性。模型为静态形式,明确排除推理与修正过程,旨在提供分析信念系统内部组织的基础框架,包括一致性条件、认知张力及表征局限。通过分离信念结构与信念强度,该形式化为认知状态的分类提供了比现有概率、逻辑或论证方法更丰富的视角。

原文摘要 · Abstract (English)

Belief systems are often treated as globally consistent sets of propositions or as scalar-valued probability distributions. Such representations tend to obscure the internal structure of belief, conflate external credibility with internal coherence, and preclude the modeling of fragmented or contradictory epistemic states. This paper introduces a minimal formalism for belief systems as directed, weighted graphs. In this framework, nodes represent individual beliefs, edges encode epistemic relationships (e.g., support or contradiction), and two distinct functions assign each belief a credibility (reflecting source trust) and a confidence (derived from internal structural support). Unlike classical probabilistic models, our approach does not assume prior coherence or require belief updating. Unlike logical and argumentation-based frameworks, it supports fine-grained structural representation without committing to binary justification status or deductive closure. The model is purely static and deliberately excludes inference or revision procedures. Its aim is to provide a foundational substrate for analyzing the internal organization of belief systems, including coherence conditions, epistemic tensions, and representational limits. By distinguishing belief structure from belief strength, this formalism enables a richer classification of epistemic states than existing probabilistic, logical, or argumentation-based approaches.

信念建模图结构认知科学知识表示

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