Coherent conditional probabilities as a tool for default reasoning

This chapter provides an overview on the coherent conditional probability as a tool for the default reasoning. The concept of conditional event plays a central role for the probabilistic reasoning. An event is singled-out by a proposition, a statement that can be either true or false and a conditional event and defined by means of two propositions that is a multi-valued entity related to a conditional probability. The simple approach is named as Occam's razor. The chapter generalizes the idea of de Finetti related to conditional event E\H, with H ≠ 0 (the impossible event), as a three-valued logical entity (true when both E and H are true, false when H is true and E is false, ''undetermined" when H is false) by letting the third value depend on the given ordered pair (E, H) and not being just an undetermined common value for all pairs that this function can be seen as a measure of the degree of belief in the conditional event E\H, which under "natural" conditions reduces to the conditional probability P{E\H.).