We consider entailment problems involving powerful constraint languages such as guarded existential rules, in which additional semantic restrictions are put on a set of distinguished relations. We consider restricting a relation to be transitive, restricting a relation to be the transitive closure of another relation, and restricting a relation to be a linear order. We give some natural generalizations of guardedness that allow inference to be decidable in each case, and isolate the complexity of the corresponding decision problems. Finally we show that slight changes in our conditions lead to undecidability. arXiv:1607.00813v1 [cs.DB] 4 Jul 2016The size, width, and CQ-rank bounds after performing this rewriting are straightforward to check.The rewrite rules preserve the polarity of subformulas, which helps ensure that coveredness is preserved during this conversion.
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