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Partial
Semigroups
and
Convolution
Algebras
Title: |
Partial Semigroups and Convolution Algebras |
Authors:
|
Brijesh Dongol (brijesh /dot/ dongol /at/ brunel /dot/ ac /dot/ uk),
Victor B. F. Gomes (victorborgesfg /at/ gmail /dot/ com),
Ian J. Hayes (ian /dot/ hayes /at/ itee /dot/ uq /dot/ edu /dot/ au) and
Georg Struth (g /dot/ struth /at/ sheffield /dot/ ac /dot/ uk)
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Submission date: |
2017-06-13 |
Abstract: |
Partial Semigroups are relevant to the foundations of quantum
mechanics and combinatorics as well as to interval and separation
logics. Convolution algebras can be understood either as algebras of
generalised binary modalities over ternary Kripke frames, in
particular over partial semigroups, or as algebras of quantale-valued
functions which are equipped with a convolution-style operation of
multiplication that is parametrised by a ternary relation. Convolution
algebras provide algebraic semantics for various substructural logics,
including categorial, relevance and linear logics, for separation
logic and for interval logics; they cover quantitative and qualitative
applications. These mathematical components for partial semigroups and
convolution algebras provide uniform foundations from which models of
computation based on relations, program traces or pomsets, and
verification components for separation or interval temporal logics can
be built with little effort. |
BibTeX: |
@article{PSemigroupsConvolution-AFP,
author = {Brijesh Dongol and Victor B. F. Gomes and Ian J. Hayes and Georg Struth},
title = {Partial Semigroups and Convolution Algebras},
journal = {Archive of Formal Proofs},
month = jun,
year = 2017,
note = {\url{http://isa-afp.org/entries/PSemigroupsConvolution.html},
Formal proof development},
ISSN = {2150-914x},
}
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License: |
BSD License |
Status: [ok] |
This is a development version of this entry. It might change over time
and is not stable. Please refer to release versions for citations.
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