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
本文在贝尔纳普-邓恩四值逻辑FDE上推广本质与偶然模态，定义本质/偶然真、假、不一致和不确定模态，给出四值S5克里普克语义及无切超相继式演算，并证明嵌入定理，获得可靠、完全和切消除结果。
AI 中文摘要
本文研究了经典本质模态和偶然模态的多值推广。在二值逻辑中，一个命题本质为真（或假）当且仅当它真（或假）时必然为真（或假）；它偶然为真（或假）当且仅当它为真（或假）但并非必然如此。多值逻辑为引入此类进一步模态提供了自然背景。我们聚焦于贝尔纳普-邓恩的一阶蕴涵（FDE），这是一个推广经典真值的四值系统。更确切地说，我们考虑带有布尔否定和蕴涵的FDE扩展。除了本质和偶然真与假的模态外，我们还定义了本质和偶然不一致性与不确定性的模态。我们为所得逻辑提出了一种基于S5的四值克里普克语义和无切超相继式演算。然后，我们证明了这些逻辑到带有必然和可能模态的四值S5版本的语义和句法嵌入定理。这些嵌入阐明了贝尔纳普本质和偶然模态的预期解释，并产生了可靠性、完全性和切消除性结果。
英文摘要
This paper investigates many-valued generalisations of the classical essence and accident modalities. In two-valued logic, a proposition is essentially true (resp. false) if, whenever it is true (resp. false), it is necessarily true (resp. false); it is accidentally true (resp. false) if it is true (resp. false) but not necessarily so. Many-valued logics provide a natural setting for introducing further modalities of this kind. We focus on Belnap-Dunn's First-Degree Entailment (FDE), a four-valued system that generalises the classical truth values. More precisely, we consider an extension of FDE with Boolean negation and implication. In addition to modalities of essential and accidental truth and falsity, we define modalities of essential and accidental inconsistency and indeterminacy. We present a four-valued S5-based Kripke semantics and cut-free hypersequent calculi for the resulting logics. We then prove semantic and syntactic embedding theorems for these logics into a four-valued version of S5 with necessity and possibility modalities. These embeddings clarify the intended interpretation of the Belnapian essence and accident modalities and yield soundness, completeness, and cut-admissibility results.
Journal refStudia Logica, 2026
DOI：10.1007/s11225-026-10250-z
