arXiv subjects

Hugo Férée

Publications and source records attributed to Hugo Férée.

3 recordsLinked to original sources

arXiv2026

Pitts and Intuitionistic Multi-Succedent: Uniform Interpolation for KM

Pitts' proof-theoretic technique for uniform interpolation, which generates uniform interpolants from terminating sequent calculi, has only been applied to logics on an intuitionistic basis through single-succedent sequent calculi. We adapt the technique to the intuitionistic multi-succedent setting by focusing on the intuitionistic modal logic KM. To do this, we design a novel multi-succedent sequent calculus for this logic which terminates, eliminates cut, and provides a decidability argument for KM. Then, we adapt Pitts' technique to our calculus to construct uniform interpolants for KM, while highlighting the hurdles we overcame. Finally, by (re)proving the algebraisability of KM, we deduce the coherence of the class of KM-algebras. All our results are fully mechanised in the Rocq proof assistant, ensuring correctness and enabling effective computation of interpolants.

cs.LO↗

arXiv2026

A uniform characterisation of the (a)synchronous must-preorder

In the setting of message passing software, De Nicola and Hennessy must-preorder defines when a program improves on another one. Since this preorder does not come equipped with a viable proof method, using it requires an alternative relation that characterises it. The literature presents at least four different definitions of such alternative preorders, depending on whether communication is synchronous or asynchronous and on whether there is value-passing or not. The existence of these different definitions complicates the overall theory, hinders the development of tools, and, upon the whole, suggests a lack of understanding of the properties necessary and sufficient to reason on the must-preorder. This paper presents the first alternative characterisation that works at least in all the four settings mentioned above. We achieve this result thanks to an axiomatic approach that is calculus independent, by highlighting the role of blocking and non-blocking actions, and by introducing the novel notion of label abstraction. Label abstractions capture the essence of safe substitutivity w.r.t. interactions, and they let us obtain a unique proof of soundness and a unique proof of completeness that work in all the mentioned settings. We believe this generalises and simplifies the overall theory, while letting us present the existing results in a uniform way. Our proofs are constructive and our result is entirely mechanised in Rocq.

cs.LO↗

arXiv2024

Mechanised uniform interpolation for modal logics K, GL, and iSL

The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely: (1) the modal logic K, for which a pen-and-paper proof exists; (2) Gödel-Löb logic GL, for which our formalisation clarifies an important point in an existing, but incomplete, sequent-style proof; and (3) intuitionistic strong Löb logic iSL, for which this is the first proof-theoretic construction of uniform interpolants. Our work also yields verified programs that allow one to compute the propositional quantifiers on any formula in this logic.

cs.LO↗