Brett McLean

FWO Senior Postdoctoral Fellow (supervised by Andreas Weiermann and David Fernández-Duque)

Department of Mathematics: Analysis, Logic and Discrete Mathematics
Ghent University

04/2021–10/2023: postdoc on David Fernández-Duque's FWO project
Proof and Model Theory of Intuitionistic Temporal Logic
Department of Mathematics: Analysis, Logic and Discrete Mathematics
Ghent University

10/2018–03/2021: postdoc on Mai Gehrke's ERC project
Duality in Formal Languages and Logic
Laboratoire J. A. Dieudonné
Université Nice Sophia Antipolis

Publications Scholar arXiv

  1. A sound and complete axiomatisation for intuitionistic linear temporal logic (with David Fernández-Duque and Lukas Zenger)
    Principles of Knowledge Representation and Reasoning (KR), proceedings of 21st International Conference, 2024, pp. 350–360.

  2. Constructive S4 modal logics with the finite birelational frame property (with Philippe Balbiani, Martín Diéguez, and David Fernández-Duque)
    submitted, 2024, 31 pages.

  3. Complete representation by partial functions for signatures containing antidomain restriction
    International Journal of Algebra and Computation, 2024, 28 pages.

  4. Gödel–Dummett linear temporal logic (with Juan Pablo Aguilera, Martín Diéguez, and David Fernández-Duque)
    Artificial Intelligence 338 (2025), 104236.

  5. Preservation theorems for Tarski's relation algebra (with Bart Bogaerts, Balder ten Cate, and Jan Van den Bussche)
    Logical Methods in Computer Science 20 (2024), no. 3:20, 1–17.

  6. A family of decidable bi-intuitionistic modal logics (with David Fernández-Duque and Lukas Zenger)
    Principles of Knowledge Representation and Reasoning (KR), proceedings of 20th International Conference, 2023, pp. 262–271.

  7. EXPTIME-hardness of higher-dimensional Minkowski spacetime (with Robin Hirsch)
    Advances in Modal Logic, vol. 14, College Publications, 2022, pp. 491–506.

  8. A Gödel calculus for linear temporal logic (with Juan Pablo Aguilera, Martín Diéguez, and David Fernández-Duque)
    Principles of Knowledge Representation and Reasoning (KR), proceedings of 19th International Conference, 2022, pp. 2–11.

  9. Time and Gödel: fuzzy temporal reasoning in PSPACE (with Juan Pablo Aguilera, Martín Diéguez, and David Fernández-Duque)
    Workshop on Logic, Language, Information, and Computation (WoLLIC), proceedings of 28th International Workshop, Springer, 2022, pp. 18–35.

  10. Difference–restriction algebras of partial functions with operators: discrete duality and completion (with Célia Borlido)
    Journal of Algebra 604 (2022), 760–789.

  11. Difference–restriction algebras of partial functions: axiomatisations and representations (with Célia Borlido)
    Algebra Universalis 83 (2022), no. 3.

  12. A categorical duality for algebras of partial functions
    Journal of Pure and Applied Algebra 225 (2021), no. 11, 106755.

  13. Temporal logic of Minkowski spacetime (with Robin Hirsch)
    Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs, Outstanding Contributions to Logic, vol. 22, Springer, 2022, pp. 389–409.

  14. Free Kleene algebras with domain
    Journal of Logical and Algebraic Methods in Programming 117 (2020), 100606.

  15. The temporal logic of two-dimensional Minkowski spacetime with slower-than-light accessibility is decidable (with Robin Hirsch)
    Advances in Modal Logic, vol. 12, College Publications, 2018, pp. 347–366.

  16. Disjoint-union partial algebras (with Robin Hirsch)
    Logical Methods in Computer Science 13 (2017), no. 2:10, 1–31.

  17. Algebras of multiplace functions for signatures containing antidomain
    Algebra Universalis 78 (2017), no. 2, 215–248.

  18. The finite representation property for composition, intersection, domain and range (with Szabolcs Mikulás) [previously]
    International Journal of Algebra and Computation 26 (2016), no. 6, 1199–1216.

  19. Complete representation by partial functions for composition, intersection and antidomain
    Journal of Logic and Computation 27 (2017), no.4, 1143–1156.

PhD thesis