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.

翻译：在数学和计算方面,演化是一种无处不在的操作。用于亚结构性和间隙逻辑的Kripke语义学推动了其对相对于长期关系的四环值函数的研究。由此产生的关系演化概念导致定性和定量模型的二元和非元模式操作者普遍化,以及更传统的变体,因为代际关系产生于部分半组的特性。基于革命的分类、线性及发病(分数或间距)碎片的语义学作为定性应用。量化的例子包括持续时间的代数和持续时间计数的中值。