2026-07-21T14:12:44Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:23564 2025-07-28T05:57:18Z ddc:004 open_access

String Diagrams for Graded Monoidal Theories, with an Application to Imprecise Probability Sarkis, Ralph Zanasi, Fabio string diagrams graded categories probability nondeterminism We introduce string diagrams for graded symmetric monoidal categories. Our approach includes a definition of graded monoidal theory and the corresponding freely generated syntactic category. Also, we show how an axiomatic presentation for the graded theory may be modularly obtained from one for the grading theory and one for the base category. The Para construction on monoidal actegories is a motivating example for our framework. As a case study, we show how to axiomatise a variant of the graded category ImP, recently introduced by Liell-Cock and Staton to model imprecise probability [Liell-Cock and Staton, 2025]. This culminates in a representation, as string diagrams with grading wires, of programs with primitives for nondeterministic and probabilistic choices and conditioning. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ralph Sarkis and Fabio Zanasi 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.2025.5 urn:nbn:de:0030-drops-235641 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.5 eng https://creativecommons.org/licenses/by/4.0/legalcode