Unimodular triangulations in Łukasiewicz logic: Complexity bounds of probabilistic coherence

A proof for the NP-containment for the probabilistic coherence problem over events represented by formulas of the infinite-valued Łukasiewicz logic was proposed in [1] . The geometric and combinatorial argument to prove that complexity bound contains a mistake that is fixed in the present paper. Actually we present two ways to restore that imprecise claim and, by doing so, we show that the main result of that paper is indeed valid. • The NP-containment of the coherence problem for Łukasiewicz events relies on a key lemma from [1] . • The proof of this lemma uses a proposition on polynomial bounds for denominators of rational vertices in triangulations. • The original argument contains a flaw when moving from general to unimodular triangulations. • Two alternative solutions are provided. The first is a new proof of the lemma without unimodularity. • The second solution is a variant of the proposition ensuring polynomial bounds in unimodular refinements.