What the lottery paradox tells us about default reasoning

Abstract

In this paper I argue that we do not understand the process of default reasoning. A number of examples are given which serve to distinguish different default reasoning systems. It is shown that if we do not make our assumptions explicit we get into trouble with disjunctive knowledge, and if we make our assumptions explicit, we run foul of the lottery paradox. None of the current popular default reasoning systems work on all of the examples. It is argued that the lottery paradox does arise in default reasoning and can cause problems. It is also shown that some of the intuitively plausible requirements for default reasoning are incompatible. How different systems cope with this is discussed. 1 Introduction Default reasoning is the ability to jump to a conclusion based on the lack of evidence to the contrary. Deduction in standard logic does not allow such reasoning; if some proposition follows from a set of axioms, it follows from a superset of the axioms. There have been many proposal...