Wesley Fussner Researcher in logic and algebra

en ▪ fr ▪ de

My current research focuses on:

• Obtaining a systematic understanding of (Craig, deductive, uniform, Lyndon) interpolation in nonclassical logics.
• The theory of many-sorted algebras and its connection to the epistemic logic of groups.
• The structure theory of residuated lattices and what it says about the interface between substructural logics.
• Completions of ordered algebras and their applications to topological duality theory and the semantics of substructural logics.
• Interfaces between quantum and substructural logics.

I'm part of the joint DFG-GACR project CELIA and the Czech Science Foundation project MetaSuMo.

I'm currently writing a monograph with Mai Gehrke about lattice completions.

   Publications

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1. W. Fussner, G. Metcalfe, and S. Santschi, Interpolation and the Exchange Rule. Submitted manuscript, 28 pages. arXiv
2. W. Fussner and S. Santschi, Interpolation in Linear Logic and Related Systems. Submitted manuscript, 22 pages. arXiv
3. W. Fussner and N. Galatos, Semiconic Idempotent Logic II: Beth Definability and Deductive Interpolation. Submitted manuscript, 49 pages. arXiv
4. W. Fussner and N. Galatos, Semiconic Idempotent Logic I: Structure and Local Deduction Theorems. Submitted manuscript, 38 pages. arXiv
5. W. Fussner and G. Metcalfe, Transfer Theorems for Finitely Subdirectly Irreducible Algebras, J. Algebra 640:1-20 (2024), 20 pages. arXiv  published.
6. W. Fussner, Poset Products as Relational Models, Studia Logica 110:95-120 (2022), 26 pages. arXiv  published
7. W. Fussner and W. Zuluaga Botero, Some Modal and Temporal Translations of Generalized Basic Logic. In: U. Fahrenberg et al. (eds.), Proceedings of the 19th International Conference on Relational and Algebraic Methods in Computer Science (RAMiCS 2021), LNCS 13027, pp. 176-191, 17 pages. arXiv  published.
8. W. Fussner and G. St. John, Negative Translations of Orthomodular Lattices and Their Logic. In: C. Heunen and M. Backens (eds.), Proceedings of the 18th International Conference on Quantum Physics and Logic (QPL 2021), EPTCS 343, pp. 37-49, 12 pages. arXiv published
9. W. Fussner, M. Gehrke, S. van Gool, and V. Marra, Priestley Duality for MV-algebras and Beyond, Forum Mathematicum 33:899-922 (2021), 23 pages. arXiv  published
10. W. Fussner and P. Jipsen, Distributive Laws in Residuated Binars, Algebra Universalis 80, paper 54 (2019), 13 pages. arXiv  published
11. W. Fussner and N. Galatos, Categories of models of R-mingle, Ann. Pure Appl. Logic 170:1188-1242 (2019), 55 pages. arXiv  published
12. W. Fussner and A. Palmigiano, Residuation Algebras with Functional Duals, Algebra Universalis 80, paper 40 (2019), 10 pages. published
13. W. Fussner and S. Ugolini, A Topological Approach to MTL-algebras, Algebra Universalis 80, paper 38 (2019), 37 pages. arXiv  published
14. W. Fussner and A. Palmigiano, Residuation Algebras with Functional Duals. In: K. Adaricheva, W. DeMeo, and J. Hyndman (eds.), Algebras and Lattices in Hawai'i: Honoring Ralph Freese, Bill Lampe, and J.B. Nation, pp. 39-46, Lulu 2018, 7 pages. arXiv  published
15. G. Bezhanishvili and W. Fussner, An Introduction to Symbolic Logic, Convergence, July 2013, 23 pages. published

   Thesis

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• D.W. Fussner, Categories of Residuated Lattices, PhD Thesis, University of Denver, Electronic Theses and Dissertations 1527 (November 2018). 221 pages. pdf    published

   Technical reports

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1. W. Fussner and B. Schminke, Mining Counterexamples for Wide-Signature Algebras With an Isabelle Server. In: M. Douglas et al. (eds.), Proceedings of the 6th Conference on Artificial Intelligence and Theorem Proving (AITP 2021). Short paper. arXiv  proceedings
2. W. Fussner, Computer-Assisted Identification of Splittings in Subvariety Lattices. In: C. Hales et al. (eds.), Proceedings of the 5th Conference on Artificial Intelligence and Theorem Proving (AITP 2020). proceedings
3. W. Fussner, N. Ghannoum, T. Jakl, and C. Simpson, Classification of Finite Semigroups and Categories Using Computational Methods. In: C. Hales et al. (eds.), Proceedings of the 5th Conference on Artificial Intelligence and Theorem Proving (AITP 2020). proceedings

   Some recent talks

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1. A Tour of Substructural Interpolation, Seminar on Applied Mathematical Logic, Prague, Czechia. slides
2. Interpolation in Substructural Logics II: Logics without Exchange, MOSAIC 2023, Vienna, Austria. slides
3. Interpolation in exchange-free logics, CLoCk 2023, Cracow, Poland (invited talk). slides
4. Poset Product Representations Over Simple Residuated Lattices, RAMiCS 2023, Augsburg, Germany. slides
5. Strict Implication Over Logics Without Contraction, Advances in Modal Logic 2022, Rennes, France. slides
6. Interpolation via Finitely Subdirectly Irreducible Algebras, Fourth Workshop on Interpolation, Haifa, Israel. slides
7. Representations by Antichain Labelings, BLAST 2022, Orange, California, USA (Invited talk). slides
8. The Structure of Totally Ordered Idempotent Residuated Lattices, TACL 2022, Coimbra, Portugal. slides