Causal Kripke models

Abstract In causal reasoning literature, the term actual causality is used to refer to the causality of some specific event that actually happened. One of the most prominent approaches for reasoning about actual causality is that of causal models developed by Halpern and Pearl (Pearl, Causality 2009, Halpern, British Journal for the Philosophy of Science 2005, Halpern, British Journal for the Philosophy of Science 2005). In this work, we extend Halpern and Pearl’s models for actual causality to an environment of possible world semantics. In this environment, we introduce a logic of actual causality with modal operators and provide sound and (weakly) complete axiomatization for this logic. This logic can be used for reasoning about causality in scenarios involving multiple possibilities, uncertainty and knowledge. Based on this new framework, we define what it means for an agent’s knowledge or lack of knowledge of some event to be an actual cause of some other event. We provide several examples to illustrate that our framework and definitions provide an intuitive environment to reason about actual causality in these scenarios.