Research

Research Papers

1. McDonald, J.: Spectral and pairwise Stone duality for De Morgan algebras with commutative closure operators. Under preparation.  
2. McDonald, J.: Completeness and bisimulation invariance of distributed epistemic Gödel logic over [0,1]-valued Kripke models. Under preparation 
3. McDonald, J.: Monadic and cylindric expansions of bounded implication algebras. Under review at Journal of Pure and Applied Algebra
4. McDonald, J.: Duality for partial orthomodular lattices. Under review at Algebra Universalis 
5. McDonald, J.: Cylindric quasi-implication algebras. Under review at Journal of Applied Non-Classical Logics 
6. McDonald, J.: Canonical completion and duality for cylindric ortholattices and cylindric Boolean algebras. Studia Logica (2026). https://doi.org/10.1007/s11225-026-10234-z
7. Lin, C.Y., McDonald, J.: Functional monadic ortholattices and locally finite σ-free polyadic ortholattices. Algebra Universalis. vol. 87  (2025). https://doi.org/10.1007/s00012-025-
8. McDonald, J.: Orthogonality relations and operators on bounded quasi-implication algebras. Order. vol. 42 (2025). https://doi.org/10.1007/s11083-025-09706-z
9. Harding, J., McDonald, J., Peinado, M.: Monadic ortholattices: completions and duality. Algebra Universalis. vol. 86 (2025). https://doi.org/10.1007/s00012-025-00889-5
10. McDonald, J.: Direct and ordinal products realized by triangular norm operators with no zero divisors. Fuzzy Sets and Systems. vol. 493-494 (2024). https://doi.org/10.1016/j.fss.2024.109096
11. McDonald, J., Bimbó, K.: Topological duality for orthomodular lattices. Mathematical Logic Quarterly. vol  69 (2023). https://doi.org/10.1002/malq.202200044
12. McDonald, J., Yamamoto, K.: Choice-free duality for orthocomplemented lattices by means of spectral spaces. Algebra Universalis. vol. 83 (2022). https://doi.org/10.1007/s00012-022-00789-y

PhD Thesis: Representation of Ortholattice-Based Algebras and Related Topics, University of Alberta, 2025.