---
title: "Extending Decidable Cases for Rules with Existential Variables"
authors:
  - "Jean-François Baget"
  - "Michel Leclère"
  - "Marie-Laure Mugnier"
  - "Eric Salvat"
doi: ""
url: "https://ijcai.org/proceedings/2009/118"
pdf: "https://ijcai.org/proceedings/2009/0118.pdf"
venue: "Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence"
year: 2009
pages: "677-681"
track: ""
keywords:
---

# Extending Decidable Cases for Rules with Existential Variables

Jean-François Baget, Michel Leclère, Marie-Laure Mugnier, Eric Salvat

*Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence*, pages 677-681.

## Abstract

In rules considered in this paper, the conclusion may contain existentially quantified variables, which makes reasoning tasks (as deduction) non-decidable. These rules have the same logical form as TGD (tuple generating dependencies) in databases and as conceptual graph rules. We extend known decidable cases by combining backward and forward chaining schemes, in association with a graph that captures exactly the notion of dependency between rules. Finally, we draw a map of known decidable cases, including an extension obtained by combining our approach with very recent results on TGD.Jean-François Baget, Michel Leclère, Marie-Laure Mugnier, Eric Salvat