The Limits of Fixed-Order Computation

Fixed-order computation rules, used by Prolog and most deductive database systems, do not suuce to compute the well-founded semantics 29] because they cannot properly resolve loops through negation. This inadequacy is reeected both in formulations of SLS-resolution 17, 23] which is an ideal search strategy, and in more practical strategies like SLG 5], or Well-Founded Ordered Search 27]. Typically, these practical strategies combine an inexpensive xed-order search with a relatively expensive dynamic search, such as an alternating xed point 28]. Restricting the search space of evaluation strategies by maximizing the use of xed-order computation is of prime importance for eecient goal-directed evaluation of the well-founded semantics. Towards this end, the theory of modular stratiication 24], formulates a subset of normal logic programs whose literals can be statically reordered so that the program can be evaluated using a xed-order computation rule. The class of modularly stratiied programs, however, is not closed under simple program transformations such as the HiLog transformation. We address the limits of xed-order computation by adapting results of Przymusinski 17] to formulate the class of left-to-right dynamically stratiied programs, and show that this class properly includes other classes of xed-order stratiied programs. We then introduce S LG strat , a variant of SLG resolution that uses a xed-order computation rule, and prove that it correctly evaluates ground left-to-right dynamically stratiied programs. Finally, we indicate how S LG strat can be used as a basis for computing the well-founded semantics through a search strategy called S LG RD , for SLG with Reduced use of Delaying.