Abstract 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.

中文翻译：

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Modus tollens 关于单范式：U-Modus Tollens

摘要 在模糊逻辑和近似推理中，Modus Tollens 给出的推理规则通常推导出涉及三个逻辑运算符的不等式：合取、蕴涵函数和否定。到目前为止，在这种情况下，连接通常由 t 范数建模，但最近已经指出了使用更一般连接的可能性。在这项工作中，我们想通过使用合取单范数而不是 t 范数来推广 Modus Tollens 不等式，从而得到所谓的 U-Modus Tollens。首先，我们对蕴涵函数的这种新性质进行了一般性研究，然后我们专门研究了从单项推导出的残差蕴涵。在所有情况下，