Diverse confidence levels in a probabilistic semantics for conditional logics

摘要

It has long been known that several popular default and conditional logics exactly describe infinitesimal probability constructs which betoken virtual certainty regarding the truth of one sentence if some other sentence is true. That the rules for default inference also describe a scheme of approximate inference for all positive-valued conditional probabilities has also long been known. More recently, a class of standard probability measures has been found whose expression of more likely than not is exactly described by default rules. This class can be extended by straightforward algebra so that the range of confidence levels expressed by standard probability distributions which are exactly described by the rules is as complete as for the approximate methods.