Logical Desiderata on Statistical Inference

It is common to refer to statistics as “the logic of science”. This note can be seen as an attempt to take the dictum seriously. To do so we ask which properties are desirable for a (formal) logic of statistical inference. The question is potentially as vast as science itself, so for the present occasion we set ourselves the modest aim of framing it in a way which, we hope, can be of interest both to logicians and to statisticians.