用代数框架统一定义条件独立性，提升逻辑推理效率
An Algebraic Notion of Conditional Independence, and Its Application to Knowledge Representation (full version)
- 基于逼近不动点理论构建语言无关的条件独立性
- 将全局推理拆解为并行局部推理，实现固定参数可处理
- 适用于正常逻辑编程，适配知识表示与高效推理场景
条件独立性是概率建模与高效推理的核心概念，在知识表示中也应用于命题逻辑和信念修正等特定形式系统。本文在逼近不动点理论的代数框架下研究条件独立性，提供一种语言无关的定义，可直接应用于任何具有不动点语义的逻辑系统。该定义使全局推理可转化为并行的局部推理实例，从而获得固定参数可处理性结果。同时讨论了其与现有条件独立性概念的关系，并将其应用于正常逻辑编程。
原文摘要 · Abstract (English)
Conditional independence is a crucial concept supporting adequate modelling and efficient reasoning in probabilistics. In knowledge representation, the idea of conditional independence has also been introduced for specific formalisms, such as propositional logic and belief revision. In this paper, the notion of conditional independence is studied in the algebraic framework of approximation fixpoint theory. This gives a language-independent account of conditional independence that can be straightforwardly applied to any logic with fixpoint semantics. It is shown how this notion allows to reduce global reasoning to parallel instances of local reasoning, leading to fixed-parameter tractability results. Furthermore, relations to existing notions of conditional independence are discussed and the framework is applied to normal logic programming.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。