The logic of p-values

Wagenmakers et al. addressed the illogic use of p-values in 'Psychological Science under Scrutiny'. While historical criticisms mostly deal with the illogical nature of null hypothesis significance testing (NHST), Wagenmakers et al. generalize such argumentation to the p-value itself. Unfortunately, Wagenmakers et al. misinterpret the formal logic basis of tests of significance (and, by extension, of tests of acceptance). This article highlights three instances where such logical interpretation fails and provides plausible corrections and further clarification