arXiv:2504.16938cs.AIcs.LO2025-04

将非单调推理引入形式概念分析,提升异常数据下的推断能力。

Rational Inference in Formal Concept Analysis

  • 基于KLM框架构建形式概念分析中的可反驳条件推理
  • 保持非单调推理核心原则,支持含异常数据的合理推断
  • 相比命题逻辑更注重上下文,得出更相关的结论

可反驳条件句是一种非单调推理形式,用于表达如“若ϕ,通常ψ”之类的语句。KLM框架通过构造可能世界上的优先序,为命题型可反驳条件句提供语义。这种语义所诱导的推理模式由满足非单调推理理想性质的蕴涵关系刻画。在形式概念分析(FCA)中,蕴含关系用于描述属性间的依赖,但此类蕴含不适用于存在错误或异常的数据。直到最近,FCA中的非单调推理仍基本未被研究。本文提出一种在FCA中实现KLM框架的可反驳推理构造,并证明该构造忠实于原始框架的非单调推理原则。进一步论证表明,在保持原始非单调推理思想一致的前提下,我们提出的FCA可反驳推理提供了更注重上下文的推断视角,相较于命题情形能得出更相关、更合理的结论。

原文摘要 · Abstract (English)

Defeasible conditionals are a form of non-monotonic inference which enable the expression of statements like "if $ϕ$ then normally $ψ$". The KLM framework defines a semantics for the propositional case of defeasible conditionals by construction of a preference ordering over possible worlds. The pattern of reasoning induced by these semantics is characterised by consequence relations satisfying certain desirable properties of non-monotonic reasoning. In FCA, implications are used to describe dependencies between attributes. However, these implications are unsuitable to reason with erroneous data or data prone to exceptions. Until recently, the topic of non-monotonic inference in FCA has remained largely uninvestigated. In this paper, we provide a construction of the KLM framework for defeasible reasoning in FCA and show that this construction remains faithful to the principle of non-monotonic inference described in the original framework. We present an additional argument that, while remaining consistent with the original ideas around non-monotonic reasoning, the defeasible reasoning we propose in FCA offers a more contextual view on inference, providing the ability for more relevant conclusions to be drawn when compared to the propositional case.

非单调推理形式概念分析可反驳条件

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