Title Relations into algebras of probabilistic distributions

The paper proposes two types of convex relations into algebras of probabilistic distributions as a relational algebraic foundation of semantic domains of probabilistic systems [4, 7, 8]. Following previous results by Tsumagari [16], we particularly focus on the associative law for the convex compositions defined via bounded combinations of probabilistic distributions, and prove that the convex compositions are associative for convex relations.