From Onions to Broccoli: Generalizing Lewis's counterfactual logic Patrick Girard Abstract: We present a generalization of Segerberg?s onion semantics for belief revision, in which the linearity of the spheres need not occur. The resulting logic is called broccoli logic. We provide a minimal relational logic, introducing a new neighborhood semantics operator. We then show that broccoli logic is a well-known conditional logic, the Burgess-Veltman minimal conditional logic.