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
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)