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A Kleene Algebra with Tests for Union Bound Reasoning About Probabilistic Programs Gomes, Leandro Baillot, Patrick Gaboardi, Marco Kleene algebras with tests Hoare logic equational reasoning probabilistic programs union bound formal verification Kleene Algebra with Tests (KAT) provides a framework for algebraic equational reasoning about imperative programs. The recent variant Guarded KAT (GKAT) allows to reason on non-probabilistic properties of probabilistic programs. Here we introduce an extension of this framework called approximate GKAT (aGKAT), which equips GKAT with a partially ordered monoid (real numbers) enabling to express satisfaction of (deterministic) properties except with a probability up to a certain bound. This allows to represent in equational reasoning "à la KAT" proofs of probabilistic programs based on the union bound, a technique from basic probability theory. We show how a propositional variant of approximate Hoare Logic (aHL), a program logic for union bound, can be soundly encoded in our system aGKAT. We then illustrate the use of aGKAT with an example of accuracy analysis from the field of differential privacy. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Leandro Gomes and Patrick Baillot and Marco Gaboardi 2025 Is Part Of LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2025.35 urn:nbn:de:0030-drops-227929 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.35 eng https://creativecommons.org/licenses/by/4.0/legalcode