Reality,locality, and probability

It is frequently argued that reality and locality are incompatible with the predictions of quantum mechanics. Various investigators have used this as evidence for the existence of hidden variables. However, Bell's inequalities seem to refute this possibility. Since the above arguments are made within the framework of conventional probability theory, we contend that an alternative solution can be found by an extension of this theory. Elaborating on some ideas of I. Pitowski, we show that within the framework of a generalized probability theory, reality, locality, hidden variables, and the predictions of quantum mechanics can be maintained together. Although our principal model in this work is a spin system, there are indications that this program can be extended to more general systems.