Chronological ignorance: Experiments in nonmonotonic temporal reasoning

摘要

We offer solutions to two problems in formal temporal reasoning, the qualification problem and the extended prediction problem, which, as argued in [22], subsume the infamous frame problem. The solutions make use of nonmonotonic logics. In particular, we advocate the use of a new nonmonotonic logic, the logic of chronological ignorance. On the practical level, we demonstrate the utility of the logic in specific cases. On the more theoretical level, we identify classes of theories in the logic that have nice properties: they each have a model that is (in a certain sense) unique, and those models can be computed very easily. The first class, causal theories, is sufficiently expressive to solve the qualification problem. It also suggests a new account of the intuitive notion of causation, although we do not discuss that in depth. This class is then generalized to the class of inertial theories, which are sufficiently expressive to solve also the extended prediction problem. Inertial theories embody the concept of potential histories, which are the way the world tends to behave “naturally.”