Brijesh Dongol ; Ian J. Hayes ; Georg Struth - Convolution Algebras: Relational Convolution, Generalised Modalities and Incidence Algebras

lmcs:3769 - Logical Methods in Computer Science, February 9, 2021, Volume 17, Issue 1 - https://doi.org/10.23638/LMCS-17(1:13)2021
Convolution Algebras: Relational Convolution, Generalised Modalities and Incidence Algebras

Authors: Brijesh Dongol ; Ian J. Hayes ; Georg Struth

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.


Volume: Volume 17, Issue 1
Published on: February 9, 2021
Accepted on: January 13, 2021
Submitted on: July 6, 2017
Keywords: Computer Science - Logic in Computer Science


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