The Well-Founded Semantics Is the Principle of Inductive Definition, Revisited

ABSTRACT. In the past, there have several attempts to explain logic programming under the well-founded semantics as a logic of inductive definitions. A weakness in all is the absence of an obvious connection between how we understand various types of informal inductive definitions in mathematical texts and the complex mathematics of the well-founded semantics. In this paper, we close this gap and show in a more definitive way that indeed, the well-founded semantics is a formalization of the principle of inductive definition.