Publications

Victoria Vollmer, Danielle Marshall, Harley Eades III, & Dominic Orchard. A Mixed Linear and Graded Logic: Proofs, Terms, and Models. 33rd EACSL Annual Conference on Computer Science Logic. (CSL 2025). arxiv

Victoria Vollmer, Marco Paviotti, & Dominic Orchard. On the 2-category of Graded Monads. Under review

Ongoing Projects

(Thesis) “From Graded Categorical Foundations to the Categorical Foundation of Grading” This thesis starts from a motivation for a adjoint style mixed logic for graded systems and developes the necessary foundations for a category of graded monads and a framework for graded multicategories models of graded systems.

Foundations of Graded Monads: Foundations of graded monads: Joint work with Dominic and Marco on the 2-category of graded monads, distributive laws for graded monads, and free constructions. The initial draft on the theoretical core has been submitted and we are continuing with another paper applying the free graded monad to effect systems.

Generalized Multicategories for Graded Monads: Joint work with Dominic Orchard which extends the generalized multicategories of Hermida and Leinster. We take a cartesian graded monad and define the category of multicategories whose structure is defined by that graded monad.

A Container Calculus for Schemaless Databases: Joint work with Elena Botoeva on a monadic calculus encoding for MQuery-a query language for mongo db. We use the tree structure of JSON documents formulated as both a monad and a container to encode MQuery stages.

Talks

(Upcoming) CT. On the Category of Graded Monads. Baltimore, MD USA. July 2026 (abstract)

PLAS seminar. Grothendieck Construction for Graded Monads Parts 1 & 2. Kent, UK. Jan 2026

PSSL 111. Graded Monads, Graded Multicategories, and Graded Adjoint Logic. Bologna, Italy. Sep 2025

SANDWICH seminar. The 2-Category of Graded Monads. Cambridge, UK. Feb 2025

CSL 2025. A Mixed Linear and Graded Logic: Proofs, Terms, and Models. Amsterdam, Netherlands. Feb 2025 (slides)

S-REPLS 15. A Mixed Linear and Graded Logic: Proofs, Terms, and Models. Kent, UK. July 2024

SYCO. A Mixed Linear and Graded Logic. Paris, France (remote). April 2023 (slides)

Women in Logic. A Mixed Linear and Graded Logic: Proofs, Terms, and Models. August 2022. (slides)