"Statistical" First Order Conditionals

A first-order conditional logic is defined in which conditionals such as α→β are interpreted as saying that most/normal/typical objects which satisfy α satisfy β as well. This qualitative statistical interpretation is achieved by imposing additional structure on the domain of a single first-order model in the form of an ordering over domain elements and tuples, α→β then holds if all objects with property α whose ranking is minimal satisfy β as well. These minimally ranked objects represent the typical or common objects having the property α. This semantics differs from that of the more common subjective interpretation of conditionals over sets of standard first-order structures, and it provides a more natural way of modeling qualitative statistical statements, such as "most birds fly," or "normal birds fly." We provide a sound and complete axiomatization of this logic as well as a probabilistic semantics for it.