Nonmonotonic logic and statistical inference

Classical statistical inference is nonmonotonic: obtaining more evidence or obtaining more knowledge about the evidence one has can lead to the replacement of one statistical conclusion by another, or the complete withdrawal of the original conclusion. While it has long been argued that not all nonmonotonic inference can be accounted for in terms of relative frequencies or objective probabilities, there is no doubt that much nonmonotonic inference can be accounted for in this way. Here we seek to explore the close connection between classical statistical inference and default logic, treating statistical inference within the framework of default logic, and showing that nonmonotonic logic in general, and default logic in particular, needs to take account of certain features of statistical inference. Default logic must take account of statistics, but at the same time statistics can throw light on problematic cases of default inference.