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KR
2010
Springer

Walking the Decidability Line for Rules with Existential Variables

13 years 8 months ago
Walking the Decidability Line for Rules with Existential Variables
We consider positive rules in which the conclusion may contain existentially quantified variables, which makes reasoning tasks (such as Deduction) undecidable. These rules have the same logical form as TGD (tuple-generating dependencies) in databases and as conceptual graph rules. The aim of this paper is to provide a clearer picture of the frontier between decidability and non-decidability of reasoning with these rules. We show that Deduction remains undecidable with rule; then we show that none of the known abstract decidable classes is recognizable. Turning our attention to concrete decidable classes, we provide new classes and classify all known classes by inclusion. Finally, we study, in a systematic way, the question “given two decidable sets of rules, is their union decidable?”, and provide an answer for all known decidable cases except one. Research Report LIRMM 09030 (December 2009)
Jean-François Baget, Michel LeClere, Marie-
Added 19 Jul 2010
Updated 19 Jul 2010
Type Conference
Year 2010
Where KR
Authors Jean-François Baget, Michel LeClere, Marie-Laure Mugnier
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