Research Statement

My current research focuses broadly on Heyting algebras and closely related structures, with a focus on categorical and geometric aspects of these structures, with a special focus on their logical meaning.

In the last years 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 would be 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)