[Lrde Annonce] Paper published in Algebra Universalis

The following paper has been published in Algebra Universalis: Catoids and Modal Convolution Algebras Uli Fahrenberg, Christian Johansen, Georg Struth, Krzysztof Ziemiański We show how modal quantales arise as convolution algebras 𝑄𝑋 of functions from catoids X, multisemigroups equipped with source and target maps, into modal quantales value or weight quantales Q. In the tradition of boolean algebras with operators we study modal correspondences between algebraic laws in X, Q and 𝑄𝑋. The catoids introduced generalise Schweizer and Sklar’s function systems and single-set categories to structures isomorphic to algebras of ternary relations, as they are used for boolean algebras with operators and substructural logics. Our correspondence results support a generic construction of weighted modal quantales from catoids. This construction is illustrated by many examples. We also relate our results to reasoning with stochastic matrices or probabilistic predicate transformers. The paper is available at https://link.springer.com/article/10.1007/s00012-023-00805-9