We elaborate on earlier work proposing general criteria to control unfolding during partial deduction of logic programs. We study several techniques relying on more general and more powerful well-founded orderings. In particular, we extend our framework to incorporate lexicographical priorities between argument positions in, a goal. We show that this handles some remaining deficiencies in previous methods. We emphasize the development of fully automatic algorithms for finite unfolding, avoiding the use of ad hoc techniques. Through an extensive formalization, we convey an understanding of the common principles underlying the various algorithms. Finally, we exhibit how our structure-based unfolding framework can be adapted to cope with datalog-like constant manipulating predicates in a satisfactory way.
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