On May 29th 2015, I successfully defended my dissertation "Intuitionistic Rules: Admissible Rules of Intermediate Logics" at Utrecht University.

The totality of admissible rules is an invariant associated to a logic. In my dissertation, I explain how one can describe the admissible rules of a logic and I hint at several ways in which admissible rules provide one with information about a given logic. To be a bit more specific, I describe methods by means of which one can discern between those rules that are and those rules that are not admissible in certain intermediate logics. Moreover, I show that some intermediate logics can be characterised by means of their admissible rules.


The following papers were produce while I was employed as a PhD candidate at Utrecht University.

On a Problem of Friedman and its Solution by Rybakov


Rybakov proved that the admissible rules of the intuitionistic propositional calculus are decidable. We give a proof of the same theorem, using the same core idea, but couched in the many notions that have been developed in the mean time. In particular, we illustrate how the argument can be interpreted as using refinements of the notions of exactness and extendibility.

Finite Frames Fail

Studia Logica (2016), yet to appear in print.

Many intermediate logics, even extremely well-behaved ones such as the intuitionistic propositional calculus, lack the finite model property for admissible rules. We give conditions under which this failure holds. We show that frames which validate all admissible rules necessarily satisfy a certain closure condition, and we prove that this condition, in the finite case, ensures that the frame is of width 2. Finally, we indicate how this result is related to some classical results on finite, free Heyting algebras.

Admissibility and Refutation

Archive for Mathematical Logic (2014) 53:7, 779-808

Refutation systems are formal systems for inductively arriving at the non-derivability of formulae. In particular one can use refutation systems to syntactically characterise logics. In this paper we explore the close connection between refutation systems and admissible rules. We develop technical machinery to construct refutation systems, employing techniques from the study of admissible rules. Concretely we provide a refutation system for the intermediate logics of bounded branching, known as the Gabbay-de Jongh logics. To illustrate the technique we also provide a refutation system for Medvedev's logic.

The Admissible Rules of BD2 and GSc

To appear in Notre Dame Journal of Formal Logic

The Visser rules form a basis of admissibility for the intuitionistic propositional calculus. We show how one can characterise the existence of covers in certain models by means of formulae. Trough this characterisation we provide a new proof of the admissibility of a weak form of the Visser rules. Finally, we use this observation coupled with a description of a generalisation of the disjunction property to provide a basis of admissibility for the intermediate logics BD2 and GSc.

A Note on Extensions

Lecture Notes in Computer Science (2013), 7734, pp 206-218

Any intermediate logic with the disjunction property admits the Visser rules if and only if it has the extension property. This equivalence restricts nicely to the extension property up to n. In this paper we demonstrate that the same goes even when omitting the rule ex falso quod libet, that is, working over minimal rather than intuitionistic logic. We lay the groundwork for providing a basis of admissibility for minimal logic, and tie the admissibility of the Mints-Skura rule to the extension property in a stratified manner.


During my time as a PhD candidate at Utrecht University, I gave talks on numerous occasions. A selection can be found below.

Describing Admissible Rules

April 28th 2014, Delft, The Netherlands

This is a 45 minute talk that I gave in the Applied Logic Seminar held at TU Delft. In this talk, I presented some of the machinery to describe admissible rules. A description of the admissible rules of the intermediate logic complete with respect to frames of height at most two is given. This talk is based on the work in "The Admissible Rules of BD2 and GSc".

On the Admissible Rules of Gabbay-de Jongh Logics

July 12th 2012, Manchester, UK

Talk at the 2012 Logic Colloquium. An intermediate logic which enjoys the disjunction property admits the nth de Jongh rule if and only if it has the nth extension property. The (n+1)th de Jongh rule is a basis of admissibility for the nth Gabbay-de Jongh Logic. In this talk, I introduced the de Jongh rules and indicated how one could prove the above two results, described in detail in the paper "On unification and admissible rules in Gabbay-de Jongh logics".

Characterizing Admissible Rules

June 13th 2012, Pisa, Italy

Talk at the Pisa Summer Workshop on Proof Theory. An intermediate logic which enjoys the disjunction property admits the nth de Jongh rule if and only if it has the nth extension property. In this talk, I introduced the de Jongh rules and indicated how one can prove the aforementioned correspondence.


March 24th 2012, Utrecht, The Netherlands

The student-association for Artificial Intelligence in Utrecht, USCKI Incognito organises the bi-annual "ouderdag" where parents of students can see what the programme is about. I was invited to speak on (symbolic) logic, which plays a core part in the curriculum.

Admissible Rules, Saturation: Syntax and Semantics

April 13th 2012, Ghent, Belgium

PhDs in Logic IV was a conference organised for PhD candidates working on Logic. I spoke about some recent results regarding characterising the admissibility of a rule scheme (the de Jongh rules) with a semantic property (the extension property)