Advanced Topics: Defeasible Reasoning

The principal novelty this book brings to probability theory is a sophisticated epistemology accommodating defeasible reasoning. It is this that makes the theory of nomic probability possible. Earlier theories lacked the conceptual framework of prima facie reasons and defeaters, and hence were unable to adequately formulate principles of probabilistic reasoning. Thus far, the book has relied upon a loosely formulated account of the structure of defeasible reasoning, but that must be tightened up before the theory can be implemented. This chapter gives a more rigorous account of defeasible reasoning and compares the present theory with some related work in AI. Reasoning begins from various kinds of inputs, which for convenience I will suppose to be encoded in beliefs. Crudely put, reasoning proceeds in terms of reasons. Reasons are strung together into arguments and in this way the conclusions of the arguments become justified. The general notion of a reason can be defined as follows: (2.1) A set of propositions {P1,...,Pn} is a reason for S to believe Q if and only if it is logically possible for S to be justified in believing Q on the basis of believing P1, ...,Pn. There are two kinds of reasons-defeasible and nondefeasible. Nondefeasible reasons are those reasons that logically entail their conclusions. For instance, (P&Q) is a nondefeasible reason for P. Such reasons are conclusive reasons. P is a defeasible reason for Q just in case P is a reason for Q, but it is possible to add additional information that undermines the justificatory connection. Such reasons are called ‘prima facie reasons’. This notion can be defined more precisely as follows: (2.2) P is a prima facie reason for S to believe Q if and only if P is a reason for S to believe Q and there is an R such that R is logically consistent with P but (P&R) is not a reason for S to believe Q.