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THE UNIFICATION TYPE OF ŁUKASIEWICZ LOGIC WITH A BOUNDED NUMBER OF VARIABLES
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- Journal:
- The Journal of Symbolic Logic , First View
- Published online by Cambridge University Press:
- 08 October 2025, pp. 1-18
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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
$n\geqslant 2$ 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 
$m,n \geqslant 2$ is nullary.
