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
Pre-Printed Notes
Medvedev logic is undecidable
Authors: R.N. Almeida and S. B. Knudstorp
• Submitted on 11 September 2026 (v1)
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)