Definability and commonsense reasoning

AbstractThe definition of concepts is a central problem in commonsense reasoning. Many themes in nonmonotonic reasoning concern implicit and explicit definability. Implicit definability in nonmonotonic logic is always relative to the context—the current theory of the world. We show that fixed point equations provide a generalization of explicit definability, which correctly captures the relativized context. Theories expressed within this logical framework provide implicit definitions of concepts. Moreover, it is possible to derive these fixed points entirely within the logic