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arXiv · 2504.19011

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

Marco Abbadini·Luca Spada
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Abstract

Building on the correspondence between finitely axiomatised theories in {\L}ukasieiwcz logic and rational polyhedra, we prove that the unification type of the fragment of {\L}ukasiewicz 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 {\L}ukasiewicz logic for all $m,n \geq 2$ is nullary.

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Marco Abbadini, Luca Spada. 2025-04-26. The unification type of Lukasiewicz logic with a bounded number of variables. https://arxiv.org/abs/2504.19011

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