Presenting Convex Sets of Probability Distributions by Convex Semilattices and Unique Bases ((Co)algebraic pearls)

Authors Filippo Bonchi, Ana Sokolova, Valeria Vignudelli

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Filippo Bonchi
  • University of Pisa, Italy
Ana Sokolova
  • University of Salzburg, Austria
Valeria Vignudelli
  • Univ Lyon, CNRS, ENS Lyon, UCB Lyon 1, LIP, France

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Filippo Bonchi, Ana Sokolova, and Valeria Vignudelli. Presenting Convex Sets of Probability Distributions by Convex Semilattices and Unique Bases ((Co)algebraic pearls). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We prove that every finitely generated convex set of finitely supported probability distributions has a unique base. We apply this result to provide an alternative proof of a recent result: the algebraic theory of convex semilattices presents the monad of convex sets of probability distributions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Axiomatic semantics
  • Theory of computation → Categorical semantics
  • Convex sets of distributions monad
  • Convex semilattices
  • Unique base


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