We generalize the QSQR evaluation method to give a set-oriented depth-first evaluation method for Horn knowledge bases. The resulting procedure closely simulates SLD-resolution (to take advantages of the goal-directed approach) and highly exploits set-at-a-time tabling. Our generalized QSQR evaluation procedure is sound, complete, and tight. It does not use adornments and annotations. To deal with function symbols, our procedure uses iterative deepening search which iteratively increases term depth bound for atoms occurring in the computation. When the term depth bound is fixed, our evaluation procedure runs in polynomial time in the size of extensional relations.
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