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.

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