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

2025/04/26 by Abbadini, Marco, Spada, Luca
#52B20 #57M10 #FOS: Mathematics #Logic (math.LO) #Primary: 06D35. Secondary: 03C05

paper · doi:10.48550/arxiv.2504.19011

Abstract

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≥ 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 ≥ 2 is nullary.

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