The coherence of Łukasiewicz assessments is NP-complete

Authors:
Simone Bova;Tommaso Flaminio
Affiliations:
Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, 37240-001 Nashville, TN, USA;Department of Mathematics and Computer Science, University of Siena, Pian dei Mantellini 44, I-53100 Siena, Italy
Venue:
International Journal of Approximate Reasoning
Year:
2010

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Abstract

The problem of deciding whether a rational assessment of formulas of infinite-valued Lukasiewicz 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].