Research Statement

My research focuses broadly on Heyting algebras, provability algebras, and closely related structures, studying their categorical, geometric and logical aspects of these structures. My current focus lies in several properties of the algebras of the system GLP.

In the last years, especially throughout my PhD, my interest has been mostly in the broad area "definability theory": the study of which structures can be expressed in specific formal systems. This includes questions such as (uniform) interpolation, unification, definability of higher-order quantifiers, implicit operations and connectives, elimination of imaginaries and Galois theory. My long-term goal is to develop a geometrically-inspired theory of these phenomena in non-classical logics.

In a previous academic life I was a researcher in sociology of culture. I worked on policy analysis and briefly on agent-based modelling. You can find most of my work related to that in this link.

Published Articles

Coequivalence relations and descent in modal logic

Authors: R.N. Almeida and Matteo De Berardinis

Proceedings of AIML 2026. • April 2026

Uniform local tabularity in intuitionistic logic

Authors: R.N. Almeida

Proceedings of AIML 2026. Extended version available here. • April 2026

Maximality Principles in Modal Logic and the Axiom of Choice

Authors: Rodrigo Nicolau Almeida, Guram Bezhanishvili

Fundamenta Mathematicae, Volume 271, October 2025, Pages 173-193 • 2025

A Coalgebraic Semantics for Intuitionistic Modal Logic

Authors: Rodrigo Nicolau Almeida, Nick Bezhanishvili

Advances in Modal Logic, Volume 15, August 2024, Pages 59-77 • 2024

Unification with Simple Variable Restrictions and Admissibility of Pi2-rules

Authors: Rodrigo Nicolau Almeida, Silvio Ghilardi

Advances in Modal Logic, Volume 15, August 2024, Pages 79-100 • 2024

Π2-rule systems and inductive classes of Gödel algebras

Authors: Rodrigo Nicolau Almeida

Annals of Pure and Applied Logic, Volume 176, Issue 4, April 2025 • 2025

Polyatomic logics and generalized Blok–Esakia theory

Authors: Rodrigo Nicolau Almeida

Journal of Logic and Computation, Volume 34, Issue 5, July 2024, Pages 887–935 • 2023

Accepted Articles

Esakia order-compactifications and locally Esakia spaces

Authors: R.N. Almeida, Guram Bezhanishvili and Nick Bezhanishvili

To appear in an Outstanding Contributions • Submitted on 26 Dec 2025 (v1)

Coalgebraic Semantics for Fischer Servi Intuitionistic Modal Logic

Authors: R.N. Almeida, Nick Bezhanishvili and Sarah Dukic

Accepted at CMCS 2026 • February 2026

Belief as an epistemic possibility of knowledge (and its limits)

Authors: M. Tarnowski and R.N. Almeida

Accepted at BTSK 2026. • June 2026

PDF coming soon

Pre-Printed Notes

Medvedev logic is undecidable

Authors: R.N. Almeida and S. B. Knudstorp

• Submitted on 11 September 2026 (v1)

Structural Completeness in bi-IPC

Authors: R.N. Almeida and Nick Bezhanishvili

• August 2025

Colimits of Heyting Algebras through Esakia Duality

Authors: R.N. Almeida

• Submitted on 11 September 2026 (v1); last revised 2 April 2026 (v6)

Submitted Articles

A topos for étale-finite Heyting algebras

Authors: Marco Abbadini, R.N. Almeida and Igor Arrieta

• Submitted on 2 Apr 2026 (v1); last revised 26 June 2026 (v2)

Fischer-Servi logic does not have interpolation

Authors: R.N. Almeida, Nick Bezhanishvili and Simon Lemal

• Submitted on 2 Apr 2026 (v1)

Superamalgamation for modal lattices via non-distributive dualities

Authors: R.N. Almeida, Nick Bezhanishvili and Simon Lemal

• Submitted on 25 Feb 2026 (v1)