Similarity Orders from Causal Equations

The purpose of this paper is to demonstrate that, contrary to the received wisdom, causal reasoning can be formalized wholly within the framework of Lewis’ conditional logic. To this aim we simulate causal reasoning based on structural equations in Lewis’ order semantics. This reduction is based on a formalization of an intuitive idea for computing relative similarity between worlds. Worlds are the more similar the more they satisfy the same relevant propositions, where relevance is a comparative notion represented by a preorder. In the context of causal reasoning this relevance order on propositions depends on the causal structure of the problem domain.