A Stochastic Graphs Semantics for Conditionals

Abstract

We define a semantics for conditionals in terms of stochastic graphs which gives a straightforward and simple method of evaluating the probabilities of conditionals. It seems to be a good and useful method in the cases already discussed in the literature, and it can easily be extended to cover more complex situations. In particular, it allows us to describe several possible interpretations of the conditional (the global and the local interpretation, and generalizations of them) and to formalize some intuitively valid but formally incorrect considerations concerning the probabilities of conditionals under these two interpretations. It also yields a powerful method of handling more complex issues (such as nested conditionals). The stochastic graph semantics provides a satisfactory answer to Lewis’s arguments against the PC = CP principle, and defends important intuitions which connect the notion of probability of a conditional with the (standard) notion of conditional probability. It also illustrates the general problem of finding formal explications of philosophically important notions and applying mathematical methods in analyzing philosophical issues.