A Logical Approach to Doxastic Causal Reasoning

Belief revision and causality play an important role in many applications, typically, in the study of database update mechanisms and data dependence. New contributions on causal reasoning are continuously added to the pioneering works by Pearl, Halpern and others. Though there is a long tradition of modeling belief revision in philosophical logic, the entanglement between belief revision and causal reasoning has not yet been fully studied from a logical view. In this paper, we propose a new formal logic for doxastic causal reasoning. With examples, we illustrate that our framework explains the rational way of belief revision based on causal reasoning. We further study the general properties of the logic. A complete axiomatization, as well as a decidability result, will be given. In addition, we believe our work will shed light on understanding the relation between qualitative and quantitative approaches toward (causal) dependence in general.