Causal reasoning comprises a large portion of the inference performed by automatic planners. In this paper, we consider a class of inference systems that are said to be predictive in that they derive certain causal consequences of a base set of premises corresponding to a set of events and constraints on their occurrence. The inference system is provided with a set of rules, referred to as a causal theory, that specifies, with some limited accuracy, the cause and effect relationships between objects and processes in a given domain. As modifications are made to the base set of premises, the inference system is responsible for accounting for all and only those inferences licensed by the premises and current causal theory. Unfortunately, the general decision problem for nontrivial causal theories involving partially ordered events is NP-complete. As an alternative to a complete but potentially exponential-time inference procedure, we describe a limited-inference polynomial-time algorithm capable of dealing with partially ordered events. This algorithm generates a useful subset of those inferences that will be true in all total orders consistent with some specified partial order. The algorithm is incremental and, while it is not complete, it is provably sound.