Different inferences in probabilistic logics of conditionals 'preserve' the probabilities of their premisses to different degrees. Some preserve certainty, some high probability, some positive probability, and some minimum probability. In the first case conclusions must have probability I when premisses have probability 1, though they might have probability 0 when their premisses have any lower probability. In the second case, roughly speaking, if premisses are highly probable though not certain then conclusions must also be highly probable. In the third case (...) conclusions must have positive probability when premisses do, and in the last case conclusions must be at least as probable as their least probable premisses. Precise definitions and well known examples are given for each of these properties, characteristic principles are shown to be valid and complete for deriving conclusions of each of these kinds, and simple trivalent truthtable 'tests' are described for determining which properties are possessed by any given inference. Brief comments are made on the application of these results to certain modal inferences such as "Jones may own a car, and if he does he will have a driver's license. Therefore, he may have a driver's license.". (shrink)

The semantics Vann McGee gives for his 1989 conditional logic is based on Stalnaker’s 1968 semantics but replaces the familiar concept of truth at a world with the novel concept of truth under a hypothesis. Developed here is a semantics of the standard type, in which sentences are true at worlds, only with additional constraints imposed on the accessibility relation and the selection function. McGee conditionals of the form A ⇒ X are translated into Stalnaker conditionals of the form \A (...) > X. An interpretation of the semantics is provided, and a few implications for the theory of indicative conditionals and their probabilities are noted. (shrink)