Logic Journal of the IGPL 25 (5):741-757 (2017)

Authors
Julio Michael Stern
University of São Paulo
Abstract
Although logical consistency is desirable in scientific research, standard statistical hypothesis tests are typically logically inconsistent. To address this issue, previous work introduced agnostic hypothesis tests and proved that they can be logically consistent while retaining statistical optimality properties. This article characterizes the credal modalities in agnostic hypothesis tests and uses the hexagon of oppositions to explain the logical relations between these modalities. Geometric solids that are composed of hexagons of oppositions illustrate the conditions for these modalities to be logically consistent. Prisms composed of hexagons of oppositions show how the credal modalities obtained from two agnostic tests vary according to their threshold values. Nested hexagons of oppositions summarize logical relations between the credal modalities in these tests and prove new relations.
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DOI 10.1093/jigpal/jzx024
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References found in this work BETA

The Power of the Hexagon.Jean-Yves Béziau - 2012 - Logica Universalis 6 (1-2):1-43.
Metalogical Decorations of Logical Diagrams.Lorenz6 Demey & Hans5 Smessaert - 2016 - Logica Universalis 10 (2-3):233-292.
Sur l'opposition des concepts.Robert Blanche - 1953 - Theoria 19 (3):89-130.

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