A normative account of defeasible and probabilistic inference

A good explanation among many others of logical consequence is that given a possibly empty set of assumptions A that are said to entail x, written A x, one is bound to believe x whenever it is the case that she believes the conjunction of all elements of A. This explanation shows a weak correspondence with the Tarskian semantic definition of logical consequence, according to which A entails x if and only if x is true under all interpretations (models) that make all elements of A true. But the relevant term here is "bound" ("is obliged to"), and the talk is of a normative conception of logical consequence. But where does this command come from? To understand some of the implications of what we call here a normative account of logical consequence, we will consider a notion which is not very well understood until the present day: that of "defeasible subsumption". To grasp this notion, it suffices to consider the following example.