My main current interest is to understand what is a deductive system, in what ways we can package and specify them, and what theorems we can prove from such specifications. This programme has a smaller brother, and in a way a much more deliverable task, which is to understand fragments of geometric logic.

Preprints and Publications

• 2. Bi-accessible and bipresentable 2-categories.

  Applied Categorical Structures. Oct 2024. j/w Axel Osmond.

• 1. Context, Judgement, Deduction.

  Accepted by Proceedings of CatMi 2023. May 2024. j/w Greta Coraglia.

Preprints and Publications broadly relevant to the programme

I am not the only person interested in this subject, and other authors independently from my work have been investigating this topic, below I collect some relevant work from other authors that is broadly related to these questions.

• 2. Isoregular Theories, Accessible 2-Categories, and Free Constructions.

  Nicola Gambino and Giacomo Tendas.

• 1. A 2-Sketchy Approach to Type Theory.

  Jonathan Osser.

Fragments of Geometric Logic

More about this research programme

In 2021 I started a progressive shift of my scientific interests that moved me away from formal model theory. Most of my research focus was on designing logics and deductive systems to appropriately axiomatise categories of formal models of some theory. One can look at most of my early production as an obsession for syntax-semantics dualities, completeness and reconstruction results. After some years the question of what is a logic, and what it means to specificy one replaced the original question of how to design a specific logic for a specific flavour of semantics. Hence, my broad research program is currently to understand what is a deductive system, in what ways we can package and specify them, and what we theorems we can prove from such specifications.

This programme has a smaller brother, and in a way a much more deliverable task, which is to understand Fragments of Geometric Logic, a very interesting galaxy of deductive systems. Because of its independent interest, and the effort required to work on this subproject, I created a subpage devoted to it.

Still hunting the Snark.