Causation, explanation and nonmonotonic temporal reasoning

We introduce a new approach to reasoning about action and change using nonmonotonic logic. The approach is arrived at by applying Pearl's theory of causal networks to logical formalizations of temporal reasoning domains. It handles complicated reasoning domains involving concurrent actions, actions with nondeterministic effects, preconditions over several points in time, ramification/qualification constraints and causal chains of events. Our theory comes in two versions: version ${bf S_0$ that works for logical theories in which causal knowledge is represented explicitly, and version ${bf I_0$ that works for theories in which this is not the case. We show that ${bf S_0$ can be seen as a generalization and/or correction of most existing approaches that are explicitly based on causation. Specifically, we prove that on a large class of reasoning domains, ${bf S_0$ is equivalent to McCain & Turner's theory of Ramifications and Qualifications. For another large class of reasoning domains, ${bf S_0$ turns out to be equivalent to Baral & Gelfond's ${cal L_{3$ approach. We give examples of reasoning domains that fall outside these classes and for which ${bf S_0$ yields better results than either McCain & Turner's or Baral & Gelfond's approach. We give strong arguments that ${bf S_0$ and Lin's recent causal theory are equivalent on all reasoning domains on which both are defined. For the causal approaches of Morgenstern & Stein, Geffner, Haugh and Lifschitz & Rabinov we again provide examples of reasoning domains that ${bf S_0$ handles better than they do. We also show that two of the most well-known non-causal approaches, namely Baker's account and `chronological minimization with filter preferential entailment', can be reinterpreted as approximations of ${bf I_0$. In the case of Baker we again give an equivalence theorem and a counterexample. We thus provide a reinterpretation in terms of causal network theory of much of the work done in nonmonotonic temporal reasoning.