发表机构
University of Lodz（罗兹大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文探讨依赖逻辑与三值逻辑的关联，提出两种结合经典联结词与传染性联结词的三值依赖类逻辑，并给出相应的可靠完备无切割二叉相继式演算。
AI 中文摘要
本文研究了依赖逻辑（作为关联逻辑的一个子类）与三值逻辑之间的联系。具体而言，我们识别了Epstein的主题语义与某些传染性多值逻辑所特有的变量包含条件之间的共同特征。受Del Cerro和Lugardon针对依赖逻辑的相继式演算（其中经典联结词与满足Epstein风格条件的联结词相结合）的启发，我们引入了两种三值依赖类逻辑，它们将经典合取和析取与传染性否定和蕴含相结合。我们还为这些逻辑提供了可靠、完备且无切割的二叉相继式演算。
英文摘要
In this paper, we investigate connections between dependence logics, viewed as a subclass of relating logics, and three-valued logics. More specifically, we identify common features of Epstein's subject-matter semantics and the variable-inclusion conditions characteristic of some infectious many-valued logics. Inspired by Del Cerro and Lugardon's sequent calculi for dependence logics, in which classical connectives are combined with connectives satisfying Epstein-style conditions, we introduce two three-valued dependence-like logics that combine classical conjunction and disjunction with infectious negation and implication. We also provide sound, complete, and cut-free bisequent calculi for these logics.
Journal refLogic and Logical Philosophy, 2026
