A complete tableau procedure for risk analysis

In many real-life situations making a decision entails evaluating the risks associated with the decision, which in turn requires reasoning about events and their relations. In addition to the simpler and better-understood notions of causation and precondition, in this paper we focus on block (or prevention), which is the relation established between an event φ₁ and another event φ₂ such that the number of occurrences of φ₂ decreases whenever φ₁ occurs, and mitigation, where the occurrence of φ₁ reduces the “negative” (for the particular decision we are considering) consequences of the occurrence of φ₂. By introducing two further counting operators and the notion of interval of observation, we give here a sound and complete tableau system along with a systematic tableau construction procedure.