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Abstract:

Fixed-order computation rules, used by Prolog and most deductive database systems, do not suffice to compute the well-founded semantics [29] because they cannot properly resolve loops through negation. This inadequacy is reflected 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 fixed-order search with a relatively expensive dynamic search, such as an alternating fixed point [28]. Restricting the search space of evaluation strategies by maximizing the use of fixedorder computation is of prime importance for efficient goal-directed evaluation of the wellfounded semantics. Towards this end, the theory of modular stratification [24], formulates a subset of normal logic programs whose literals can be statically reordered so that the program can be evaluated using a fixed-order computation rule. The class of modularly stratified programs, however, is not closed under simple program transformations such as the HiLog transformation. We address the limits of fixed-order computation by adapting results of Przymusinski [17] to formulate the class of left-to-right dynamically stratified programs, and show that this class properly includes other classes of fixed-order stratified programs. We then introduce SLG strat, a variant of SLG resolution that uses a fixed-order computation rule, and prove that it correctly evaluates ground left-to-right dynamically stratified programs. Finally, we indicate how SLG strat can be used as a basis for computing the well-founded semantics through a search strategy called SLGRD, for SLG with Reduced Delay.

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