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Cancellative Convex Semilattices Sokolova, Ana Woracek, Harald convex semilattice cancellativity Riesz space Convex semilattices are algebras that are at the same time a convex algebra and a semilattice, together with a distributivity axiom. These algebras have attracted some attention in the last years as suitable algebras for probability and nondeterminism, in particular by being the Eilenberg-Moore algebras of the nonempty finitely-generated convex subsets of the distributions monad. A convex semilattice is cancellative if the underlying convex algebra is cancellative. Cancellative convex algebras have been characterized by M. H. Stone and by H. Kneser: A convex algebra is cancellative if and only if it is isomorphic to a convex subset of a vector space (with canonical convex algebra operations). We prove an analogous theorem for convex semilattices: A convex semilattice is cancellative if and only if it is isomorphic to a convex subset of a Riesz space, i.e., a lattice-ordered vector space (with canonical convex semilattice operations). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ana Sokolova and Harald Woracek 2025 Is Part Of LIPIcs, Volume 342, 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CALCO.2025.12 urn:nbn:de:0030-drops-235714 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.12 eng https://creativecommons.org/licenses/by/4.0/legalcode