The unification type of Lukasiewicz logic with a bounded number of variables
Marco Abbadini, Luca Spada · arXiv (Cornell University) · 2025
Building on the correspondence between finitely axiomatised theories in Łukasieiwcz logic and rational polyhedra, we prove that the unification type of the fragment of Łukasiewicz logic with $n\geq 2$ variables is nullary. This solves a problem left open in [V. Marra and L. Spada. Ann. Pure Appl. Logic 164 2013, p. 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 $m,n \geq 2$ is nullary.