A Characterization of Probabilistic Entailment in Adams' Logic of Conditionals.

Abstract

Abstract : Ernest Adams' logic of conditionals is useful in expert systems because it can be used to reason about imperfect generalizations, i.e., generalizations of the form: In nearly all instances where a is true, b is true. This paper defines a notion of importance and then shows that Adams' logic is equivalent to a logic for reasoning about generalizations of the form: in all important instances where a is true, b is true. A new method of proving results in Adam's logic-a method based upon the importance notion-is described. This method of proof is often quite easy, particularly since Venn diagrams can be used to help find proofs. An example using this new method of proof is presented. The example shows that Adams' logic justifies a common method of conflict resolution in expert systems, namely, the specificity-wins method. Finally, it is shown that Adams' logic can be used to reason about a topic seemingly unrelated to imperfect generalizations: the choices made by rational agents.