The sufficient cause principle and reasoning about action

Most `causal' approaches to reasoning about action have not addressed the basic question of causality directly: what has to be the case in a domain in order for the assertion `$A$ causes $B$' to be valid with respect to the domain? Pearl's recent causal theories based on {em structural equations/ do provide an answer to this question. In this paper, we extend Pearl's formalism so that the typical problems encountered in common sense reasoning about action can be represented in it. The resulting theory comes in both a propositional and a first-order version. The propositional version turns out to be capable of handling many complicated instances of the ramification problem, including domains that contain cyclic causal relationships. It also provides new insights into actions with non-deterministic and/or `disjunctive' effects. The first-order version additionally handles domains with `dependent' fluents, incompletely specified action schedules, causal chains of events and `surprises'. We provide an in-depth comparison between our theory and three other recent approaches: those of McCain & Turner, Baral & Gelfond and Lin. For the former two, we show that they can be reinterpreted as approximations of our extension of Pearl's theory: we prove theorems stating that for large classes of reasoning domains, they permit the same inferences as our theory does, and we give examples of reasoning domains that fall outside these classes, for which our approach clearly works better. For the approach of Lin, we show informally that, for those reasoning domains on which both his and our approach are defined, the two approaches are nearly equivalent. In this way we are able to establish a connection between Lin's approach and Pearl's semantics of causation. Since all concepts in our theory which involve causality are defined in completely non-causal terms, we hope that our work may help bridge the conceptual gap between `causal' and `non-causal' approaches to common sense temporal reasoning.