An analysis of the equational properties of the well-founded fixed point

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and in particular to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study the logical properties of the (parametric) well-founded fixed point operation. We show that the operation satisfies several, but not all of the standard equational properties of fixed point operations described by the axioms of iteration theories.