Time in a causal theory

We present a causal theory based on an interventionist conception of causality, i.e., a preference to select causes among a set of actions which an agent has the ability to perform or not (free will). Emphasis is put on the temporal and explanatory aspects of causal reasoning. We introduce a formal framework enabling to define the notion of voluntary cause in a way allowing for an effective retrieval of causes in a given situation. The causal knowledge is represented by causal rules of two kinds: strict and "normal". The latter is based on the notions of preferred time lines (futures that the agent normally has in mind when (s)he opts for performing the action) and of inhibiting events (the occurrence of which prevents the anticipated effect to happen). A situation is described by a set of events occurring on time lines; this description is completed by default assumptions (when an agent performs an action, we assume, unless this is inconsistent, that its preconditions are fulfilled and that no inhibiting event will take place). An example is presented, extension to first-order is briefly discussed, and our approach is compared to related works.