Abstract
We introduce \(\ell r\)-multisemigroups as duals of modal quantales and study modal correspondences between equations in these multisemigroups and the domain and codomain axioms of modal quantales. Our results yield new insights on the origin of locality in modal semirings and quantales. They also yield construction principles for modal powerset quantales that cover a wide range of models and applications.
U. Fahrenberg—Supported by the Chaire ISC : Engineering Complex Systems – École polytechnique – Thales – FX – DGA – Dassault Aviation – Naval Group – ENSTA ParisTech – Télécom ParisTech.
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The third and fourth author would like to thank the Laboratoire d’informatique de l’École polytechnique, where part of this work has been conducted, for their hospitality and financial support.
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Calk, C., Fahrenberg, U., Johansen, C., Struth, G., Ziemiański, K. (2021). \(\ell r\)-Multisemigroups, Modal Quantales and the Origin of Locality. In: Fahrenberg, U., Gehrke, M., Santocanale, L., Winter, M. (eds) Relational and Algebraic Methods in Computer Science. RAMiCS 2021. Lecture Notes in Computer Science(), vol 13027. Springer, Cham. https://doi.org/10.1007/978-3-030-88701-8_6
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