World Logic Day in Aveiro

Department of Mathematics, University of Aveiro, room 11.2.21, 12th Jan, 2024



14:30 - 15:15 Leandro Gomes CRIStAL, Université de Lille, France
A KAT-like approach for union bound reasoning on probabilistic programs
Zoom link
ABSTRACT: Kleene Algebra with Tests (KAT) provides a framework for algebraic equational reasoning on 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 aGKAT (approximate GKAT), a form of graded GKAT over a partially ordered monoid (real numbers) which enables 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 on an example of accuracy analysis from the field of differential privacy.

15:30 - 16:30 Work in progress session

Local Organisers

Manuel A. Martins
Alexandre Madeira