# Walking the Decidability Line for Rules with Existential Variables

2 GRAPHIK - Graphs for Inferences on Knowledge
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : 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 a single 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.
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Reports

https://hal-lirmm.ccsd.cnrs.fr/lirmm-00441907
Contributor : Marie-Laure Mugnier <>
Submitted on : Thursday, December 17, 2009 - 3:30:53 PM
Last modification on : Wednesday, June 5, 2019 - 11:58:12 AM

### Identifiers

• HAL Id : lirmm-00441907, version 1

### Citation

Jean-François Baget, Michel Leclère, Marie-Laure Mugnier. Walking the Decidability Line for Rules with Existential Variables. RR-09030, 2009, pp.21. ⟨lirmm-00441907⟩

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