一句话：用关系卷积统一刻画子结构/区间逻辑的广义模态与关联代数语义。
卷积是数学与计算中的普遍操作。为刻画子结构逻辑和区间逻辑的 Kripke 语义，本文研究相对于三元关系的 quantale 值函数卷积。作者提出关系卷积概念，由此导出广义的二元和一元模态算子，适用于定性与定量模型；当三元关系来自偏半群上的恒等关系时，可得到更常规的模态变体。该框架为范畴逻辑、线性逻辑和关联（段或区间）逻辑的片段提供了基于卷积的语义，并给出持续时间演算中持续时间与均值代数等定量实例。论文通过统一代数视角，将关系卷积、广义模态与关联代数联系起来，展示了其在逻辑语义与定量推理中的广泛适用性。
Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantale-valued functions relative to ternary relations. The resulting notion of relational convolution leads to generalised binary and unary modal operators for qualitative and quantitative models, and to more conventional variants, when ternary relations arise from identities over partial semigroups. Convolution-based semantics for fragments of categorial, linear and incidence (segment or interval) logics are provided as qualitative applications. Quantitative examples include algebras of durations and mean values in the duration calculus.
@article{paperbot1338,
title = {Convolution Algebras: Relational Convolution, Generalised Modalities and Incidence Algebras},
author = {Brijesh Dongol and Ian J. Hayes and Georg Struth},
journal = {Logical Methods in Computer Science},
volume = {Volume 17, Issue 1},
year = {2021},
doi = {10.23638/lmcs-17(1:13)2021}
}