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00925njm 22002777a 4500 dc Aguilo, Isabel author Riera, Juan Vicente author Suner, Jaume author Torrens, Joan author 2020-12 In fuzzy logic and approximate reasoning the inference rule given by the Modus Tollens usually derives into an inequality involving three logical operators: a conjunction, an implication function and a negation. Until now, in this scenario the conjunction has been commonly modeled by a t-norm, but recently the possibility of using a more general conjunction has been pointed out. In this work, we want to generalize the Modus Tollens inequality by using a conjunctive uninorm instead of a t-norm, leading to the so-called U-Modus Tollens. First, we give a study of this new property for implication functions in general and then we specially focus on residual implications derived from uninorms. In all cases, we prove that there are a lot of solutions of the U-Modus Tollens and we give a characterization of all the solutions in some particular cases. (c) 2020 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Aguilo I, Vicente Riera J, Suner J, Torrens J. Modus tollens with respect to uninorms: U-Modus Tollens. Int J Approx Reasoning. 2020 Dec;127:54-69. 10.1016/j.ijar.2020.10.003 1873-4731 0888-613X International Journal of Approximate Reasoning http://hdl.handle.net/20.500.13003/17230 2-s2.0-85093646670 https://hdl.handle.net/20.500.12105/22902 591502900004 Modus Tollens Uninorm Implication function RU-implication Modus tollens with respect to uninorms: U-Modus Tollens