We attempt at a logical characterization of reasoning about normality based on the intuition that a normal situation is represented by a stable set of default assumptions. Within the context of preferential consequence relations we shall define a normality operator B and study its logical properties. Finally we shall focus on the AGM-like postulates for the normality expansion, contraction and ...

A number is normal to the base r if, in its expansion to that base, all possible digit strings of length t are equally frequent for each t. While it is generally believed that many familiar irrational constants are normal, normality has only been proven for numbers expressly invented for the purpose of proving their normality. In this study we give an overview of the main results to date. We th...

The article is devoted to normality assumption in statistical data analysis. It gives a short historical review of the development of scientific views on the normal law and its applications. It also briefly covers normality tests and analyzes possible consequences of using the normality assumption incorrectly.

We introduce a new class of functions called almost gs-closed and use the functions to improve several preservation theorems of normality and regularity and also their generalizations. The main result of the paper is that normality and weak normality are preserved under almost gs-closed continuous surjections.