Well-founded semantics and the algebraic theory of non-monotone inductive definitions

Approximation theory is a fixpoint theory of general (monotone and non-monotone) operators which generalizes all main semantics of logic programming, default logic and autoepistemic logic. In this paper, we study inductive constructions using operators and show their confluence to the well-founded fixpoint of the operator. This result is one argument for the thesis that Approximation theory is the fixpoint theory of certain generalised forms of (non-monotone) induction. We also use the result to derive a new, more intuitive definition of the wellfounded semantics of logic programs and the semantics of ID-logic, which moreover is easier to implement in model generators. © Springer-Verlag Berlin Heidelberg 2007.status: publishe