Rohit Parikh

We propose a model for belief which is free of presuppositions. Current models for belief suffer from two difficulties. One is the well known problem of logical omniscience which tends to follow from most models. But a more important one is the fact that most models do not even attempt to answer the question what it means for someone to believe something, and justwhatit is that is believed. We provide a flexible model which allows us to give meaning to beliefs in general contexts, including the context of animal belief (where action is usually our only clue to a belief), and of human belief which is expressed in language.

One interpretation of the conditional If P then Q is as saying that the probability of Q given P is high. This is an interpretation suggested by Adams (1966) and pursued more recently by Edgington (1995). Of course, this probabilistic conditional is nonmonotonic, that is, if the probability of Q given P is high, and R implies P, it need not follow that the probability of Q given R is high. If we were confident of concluding Q from the fact that we knew P, and we have stronger information R, we can no longer be confident of Q. We show nonetheless that usually we would still be justified in concluding Q from R. In other words, probabilistic conditionals are mostly monotonic