The unification type of Łukasiewicz logic with a bounded number of variables

Abbadini, Marco;Spada, Luca
(2025) The Journal of Symbolic Logic — (2025)

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Abstract
Building on the correspondence between finitely axiomatised theories in Łukasiewicz logic and rational polyhedra, we prove that the unification type of the fragment of Łukasiewicz logic with n ≥ 2 variables is nullary. This solves a problem left open by V. Marra and L. Spada [Ann. Pure Appl. Logic 164 (2013), pp. 192-210]. Furthermore, we refine the study of unification with bounds on the number of variables. Our proposal distinguishes the number m of variables allowed in the problem and the number n in the solution. We prove that the unification type of Łukasiewicz logic for all m, n ≥ 2 is nullary.
Affiliations
  • University of Birmingham
  • Università degli Studi di Salerno

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Abbadini, M., & Spada, L. (2025). The unification type of Łukasiewicz logic with a bounded number of variables. The Journal of Symbolic Logic. Accepted/in-press. https://doi.org/10.1017/jsl.2025.10149 (Original work published 2025)