The abnormality predicate

The author has suggested earlier that the various nonmonotonic reasoning formalisms are converging towards probability. Here, he discusses the idea of randomness: using a definition by Kyburg as a benchmark, he describes how it appears in various nonmonotonic reasoning formalisms, in particular, circumscription. It is argued that behind the complexity of circumscription lie the simple notions of random sampling and statistically founded beliefs. The latter is implemented through a device known as the abnormality predicate which appears in various guises in the nonmonotonic reasoning literature. Another view of this study is that randomness provides a universal conjecture for nonmonotonic theories. Default theories can be interpreted as jumping to the conclusion that an entity is a random member of a certain class