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Statistical Hypothesis Testing (SHT) is a class of inference methods wherebyone makes use of empirical data to test a hypothesis and often emit a judgmentabout whether to reject it or not. In this paper we focus on the logical aspectof this strategy, which is largely independent of the adopted school ofthought, at least within the various frequentist approaches. We identify SHT astaking the form of an unsound argument from Modus Tollens in classical logic,and, in order to rescue SHT from this difficulty, we propose that it caninstead be grounded in t-norm based fuzzy logics. We reformulate thefrequentists' SHT logic by making use of a fuzzy extension of modus Tollens todevelop a model of truth valuation for its premises. Importantly, we show thatit is possible to preserve the soundness of Modus Tollens by exploring thevarious conventions involved with constructing fuzzy negations and fuzzyimplications (namely, the S and R conventions). We find that under the Sconvention, it is possible to conduct the Modus Tollens inference argumentusing Zadeh's compositional extension and any possible t-norm. Under the Rconvention we find that this is not necessarily the case, but that by mixingR-implication with S-negation we can salvage the product t-norm, for example.In conclusion, we have shown that fuzzy logic is a legitimate framework todiscuss and address the difficulties plaguing frequentist interpretations ofSHT.

A fuzzy take on the logical issues of statistical hypothesis testing