The coherence of Łukasiewicz assessments is NP-complete

The problem of deciding whether a rational assessment of formulas of infinite-valued Łukasiewicz logic is coherent has been shown to be decidable by Mundici [1], and in PSPACE by Flaminio and Montagna [10], . We settle its computational complexity proving an NP-completeness result. We then obtain NP-completeness results for the satisfiability problem of certain many-valued probabilistic logics introduced by Flaminio and Montagna in [9].