From C-Believed Propositions to the Causal Calculator

Default rules, unlike inference rules of classical logic, allow us to derive a new conclusion only when it does not conflict with the other available information. The best known example is the so-called commonsense law of inertia: in the absence of information to the contrary, properties of the world can be presumed to be the same as they were in the past. Making the idea of commonsense inertia precise is known as the frame problem [Shanahan 1997]. Default reasoning is nonmonotonic, in the sense that we may be forced to retract a conclusion derived using a default when additional information becomes available. The idea of a default first attracted the attention of AI researchers in the 1970s. Developing a formal semantics of defaults turned out to be a difficult task. For instance, the attempt to describe commonsense inertia in terms of circumscription outlined in [McCarthy 1986] was unsatisfactory, as we learned from the Yale Shooting example [Hanks and McDermott 1987]. In this note, we trace the line of work on the semantics of defaults that started with Judea Pearl’s 1988 paper on the difference between “E-believed” and “Cbelieved” propositions. That paper has led other researchers first to the invention of several theories of nonmonotonic causal reasoning, then to designing action languages C and C+, and then to the creation of the Causal Calculator—a software system for automated reasoning about action and change.