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The coherence of Łukasiewicz assessments is NP-complete. (English) Zbl 1201.68117
Summary: The problem of deciding whether a rational assessment of formulas of infinite-valued Łukasiewicz logic is coherent has been shown to be decidable by D. Mundici [Theor. Comput. Sci. 52, 145–153 (1987; Zbl 0639.03042)] and in PSPACE by T. Flaminio and F. Montagna [J. Log. Comput., “Models for many-valued probabilistic reasoning”, doi:10.1093/logcom/exp013]. 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 T. Flaminio and F. Montagna in [Int. J. Approx. Reasoning 50, No. 1, 138–152 (2009; Zbl 1185.06007)].

##### MSC:
 68T37 Reasoning under uncertainty in the context of artificial intelligence 03B50 Many-valued logic 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) 68Q25 Analysis of algorithms and problem complexity
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