Reasoning with minimal models: efficient algorithms and applications
Reasoning with minimal models is at the heart of many knowledge-representation systems. Yet it turns out that this task is formidable, even when very simple theories are considered. In this paper, we introduce the elimination algorithm, which performs, in linear time, minimal model finding and minimal model checking for a significant subclass of positive CNF theories which we call positive bead-cycle-free (HCF) theories. We also prove that the task of minimal entailment is easier for positive HCF theories than it is for the class of all positive CNF theories. Finally, we show how variations of the elimination algorithm can be applied to allow queries posed on disjunctive deductive databases and disjunctive default theories to be answered in an efficient way. (C) 1997 Published by Elsevier Science B.V.
minimal models disjunctive databases disjunctive default logic disjunctive logic programs stable model semantics linear time algorithms