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 AlgebrasArticle

Authors: Brijesh Dongol ORCID; 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
    Funding:
      Source : OpenAIRE Graph
    • Verifiably correct concurrency abstractions; Funder: UK Research and Innovation; Code: EP/R019045/2
    • Discovery Projects - Grant ID: DP190102142; Funder: Australian Research Council (ARC); Code: DP190102142
    • Verifiably Correct Transactional Memory; Funder: UK Research and Innovation; Code: EP/R032556/1

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