Dongol, B., Hayes, I.J. and Struth, G. (2021) Convolution algebras: Relational convolution, generalised modalities and incidence algebras. Logical Methods in Computer Science, 17 (1). 13:1-13:34. ISSN 1860-5974
Abstract
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © B. Dongol, I. J. Hayes, and G. Struth. Article available under a Creative Commons license (http://creativecommons.org/licenses/by/4.0/). |
Keywords: | Computer Science; Logic in Computer Science |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 18 Mar 2021 13:43 |
Last Modified: | 18 Mar 2021 23:52 |
Published Version: | https://lmcs.episciences.org/7164 |
Status: | Published |
Publisher: | Logical Methods in Computer Science |
Refereed: | Yes |
Identification Number: | 10.23638/LMCS-17(1:13)2021 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:172120 |