Email Gateway (Aug 22 2022 at 15:37): Email Gateway (Aug 22 2022 at 15:37):From: Tobias Nipkow <nipkow@in.tum.de>
Partial Semigroups and Convolution Algebras
Brijesh Dongol, Victor B. F. Gomes, Ian J. Hayes and Georg Struth
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.
https://www.isa-afp.org/entries/PSemigroupsConvolution.shtml
Enjoy!
smime.p7s
Last updated: Nov 21 2024 at 12:39 UTC