通过变量出现关系重构矛盾处理框架，实现非爆炸性推理。
A Variable Occurrence-Centric Framework for Inconsistency Handling (Extended Version)
- 以变量出现为中心构建矛盾分析框架，定义最小不一致与最大一致关系
- 提出基于最大一致关系的修复策略，避免经典逻辑的爆炸问题
- 为变量出现赋予真值，适合需要精细矛盾处理的逻辑系统设计
本文提出一种用于分析和处理命题基中不一致性的语法框架。该方法聚焦于冲突中变量出现之间的关系，引入两个对偶概念：最小不一致关系（MIR）和最大一致关系（MCR）。每个MIR是使系统不一致的最小等价关系，而每个MCR是旨在防止不一致的最大等价关系。值得注意的是，MIR能够捕捉到传统最小不一致子集所遗漏的冲突。基于MCR，我们构建了一系列非爆炸性推理关系：通过根据每个MCR修改命题基，再使用经典推理关系推导结论。此外，我们提出一种非传统语义，将真值分配给变量出现而非变量本身，相关推理关系则通过与基于出现的模型相容的布尔解释建立。
原文摘要 · Abstract (English)
In this paper, we introduce a syntactic framework for analyzing and handling inconsistencies in propositional bases. Our approach focuses on examining the relationships between variable occurrences within conflicts. We propose two dual concepts: Minimal Inconsistency Relation (MIR) and Maximal Consistency Relation (MCR). Each MIR is a minimal equivalence relation on variable occurrences that results in inconsistency, while each MCR is a maximal equivalence relation designed to prevent inconsistency. Notably, MIRs capture conflicts overlooked by minimal inconsistent subsets. Using MCRs, we develop a series of non-explosive inference relations. The main strategy involves restoring consistency by modifying the propositional base according to each MCR, followed by employing the classical inference relation to derive conclusions. Additionally, we propose an unusual semantics that assigns truth values to variable occurrences instead of the variables themselves. The associated inference relations are established through Boolean interpretations compatible with the occurrence-based models.
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