Knowledge compilation is an alternative solution to address demanding reasoning tasks with high complexity via converting knowledge bases into a suitable target language. The notion of logical separability, proposed by Levesque, offers a general explanation for the tractability of clausal entailment for two remarkable languages: decomposable negation normal form and prime implicates. It is interesting to explore what role logical separability plays in problem tractability. In this paper, we apply the notion of logical separability to a number of reasoning problems within the context of propositional logic: satisfiability checking (CO), clausal entailment checking (CE), model counting (CT), model enumeration (ME) and forgetting (FO), as well as their dual tasks, contributing to several recursive procedures. We provide the corresponding logical separability based properties: CO-logical separability, CE-logical separability, CT-logical separability, ME-logical separability and their duals. Based on these properties, we then identify four novel normal forms: $\mathtt{CO}\text{-}\mathtt{LSNNF}$, $\mathtt{CE}\text{-}\mathtt{LSNNF}$, $\mathtt{CT}\text{-}\mathtt{LSNNF}$ and $\mathtt{ME}\text{-}\mathtt{LSNNF}$, as well as their dual languages. We show that each of them is the necessary and sufficient condition under which the corresponding procedure is correct. We finally integrate the above normal forms into the knowledge compilation map.

知识编译是一种替代解决方案，通过将知识库转换为合适的目标语言来解决高复杂度的推理任务。Levesque 提出的逻辑可分性概念为两种著名语言的分句蕴涵的易处理性提供了一般性解释：可分解否定范式和素数蕴涵。探索逻辑可分离性在问题可处理性中扮演什么角色是很有趣的。在本文中，我们将逻辑可分性的概念应用于命题逻辑背景下的许多推理问题：可满足性检查（CO）、子句蕴涵检查（ CE）、模型计数（ CT）、模型枚举（ ME）和遗忘( FO ) 以及它们的双重任务，促成了几个递归过程。我们提供相应的基于逻辑可分离性的属性：CO -逻辑可分离性， CE -逻辑可分离性， CT -逻辑可分离性， ME -逻辑可分离性及其对偶。基于这些属性，我们确定了四种新的范式：$\mathtt{一氧化碳}\text{-}\mathtt{LSNNF}$,$\mathtt{CE}\text{-}\mathtt{LSNNF}$,$\mathtt{CT}\text{-}\mathtt{LSNNF}$和$\mathtt{我}\text{-}\mathtt{LSNNF}$，以及他们的双语。我们证明它们中的每一个都是相应程序正确的充分必要条件。我们最终将上述范式整合到知识编译图中。