陈霖、文学锋 | Strict-tolerant conditional logics

论文题目：Strict-tolerant conditional logics

作者：陈霖、文学锋
原文链接：https://doi.org/10.1093/logcom/exag001

发表期刊：Journal of Logic and Computation, Volume 36, Number 2, March 2026
 

论文摘要：

We construct a conditional logic using selection models in a three-valued setting. When the selection function selects an empty set, the corresponding conditional is neither true nor false. The semantic consequence is defined as in strict-tolerant logic. The resulting logic validates conditional excluded middle without assuming that a selection function always chooses a single world, reconciling Stalnaker and Lewis. We give a labelled sequent calculus for the logic and consider three extensions of it. With the sequent calculus in hand, we show the decidability of two systems. It turns out that two extensions are strongly connexive, hyperconnexive, superconnexive and almost totally connexive. We compare our logics with other connexive conditional logics and show the philosophical consequence concerning paraconsistency and überconsistency.
 

成果介绍

条件句“如果……，那么……”是科学假设、反事实推理与决策推理的核心。可能世界语义学已成为分析条件句的常用框架。其中，斯塔尔纳克采用唯一性假设，即通过选择函数选出的最相似世界是唯一的；而刘易斯则允许存在多个同等相似的世界。尽管有充分理由放弃斯塔尔纳克的唯一性假设，但这会导致条件排中律这一直观原则失效。本研究提出一种新的语义框架，旨在调和二者的张力。在放弃唯一性假设的前提下，该语义通过三值选择模型与严格-宽容后承，使得条件排中律的有效性在新定义的逻辑中得以恢复。我们为该逻辑构建了可靠且完全的加标矢列演算系统，并进一步考察了它的三个扩展系统，证明了其中部分系统的可判定性。研究发现，其中两个扩展是文献中较为罕见的强连接逻辑。为此，我们系统地比较了已有的一些连接条件句逻辑。哲学上，本文提出的语义表明:在保留经典排中律和爆炸律的同时，仍可实现高度的连接性；同时也澄清了超协调性（überconsistency）、次协调性（paraconsistency）与双面真理论（dialetheism）之间错综复杂的关系。