Abstract
This paper establishes alternative characterizations of very expressive classes of existential rule sets with decidable query entailment. We consider the notable class of greedy bounded-treewidth sets (\(\textbf{gbts}\)) and a new, generalized variant, called weakly gbts (\(\textbf{wgbts}\)). Revisiting and building on the notion of derivation graphs, we define (weakly) cycle-free derivation graph sets (\(\mathbf {(w)cdgs}\)) and employ elaborate proof-theoretic arguments to obtain that \(\textbf{gbts}\) and \(\textbf{cdgs}\) coincide, as do \(\textbf{wgbts}\) and \(\textbf{wcdgs}\). These novel characterizations advance our analytic proof-theoretic understanding of existential rules and will likely be instrumental in practice.
Work supported by the ERC through Consolidator Grant 771779 (DeciGUT).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We recall that entailment of non-Boolean CQs or even query answering can all be reduced to BCQ entailment in logarithmic space.
- 2.
Beyond \((\textsf{tr})\) and \((\textsf{ar})\), we note that Baget et al. [5] introduced an additional reduction operation, referred to as arc contraction. We do not consider this rule here however as it is unnecessary to characterize \(\textbf{gbts}\) and \(\textbf{wgbts}\) in terms of derivation graphs and prima facie obstructs the proof of Theorem 2.
References
Baget, J.F.: Improving the forward chaining algorithm for conceptual graphs rules. In: Proceedings of the Ninth International Conference on Principles of Knowledge Representation and Reasoning. p. 407–414. KR’04, AAAI Press (2004)
Baget, J.F., Leclère, M., Mugnier, M.L., Salvat, E.: Extending decidable cases for rules with existential variables. In: Proceedings of the 21st International Jont Conference on Artifical Intelligence. p. 677–682. IJCAI’09, Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2009)
Baget, J.F., Leclère, M., Mugnier, M.L., Salvat, E.: Extending decidable cases for rules with existential variables. In: Proceedings of the 21st International Joint Conference on Artificial Intelligence. p. 677–682. IJCAI’09, Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2009)
Baget, J.F., Mugnier, M.L.: Extensions of simple conceptual graphs: the complexity of rules and constraints. Journal of Artificial Intelligence Research 16, 425–465 (2002)
Baget, J.F., Leclère, M., Mugnier, M.L., Salvat, E.: On rules with existential variables: Walking the decidability line. Artificial Intelligence 175(9), 1620–1654 (2011). https://doi.org/10.1016/j.artint.2011.03.002
Calì, A., Gottlob, G., Kifer, M.: Taming the infinite chase: Query answering under expressive relational constraints. Journal of Artificial Intelligence Research 48, 115–174 (2013). https://doi.org/10.1613/jair.3873
Chandra, A.K., Lewis, H.R., Makowsky, J.A.: Embedded implicational dependencies and their inference problem. In: Proceedings of the 13th Annual ACM Symposium on Theory of Computing (STOC’81). pp. 342–354. ACM (1981). https://doi.org/10.1145/800076.802488
Deutsch, A., Nash, A., Remmel, J.B.: The chase revisited. In: Lenzerini, M., Lembo, D. (eds.) Proceedings of the 27th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS’08). pp. 149–158. ACM (2008). https://doi.org/10.1145/1376916.1376938
Fagin, R., Kolaitis, P.G., Miller, R.J., Popa, L.: Data exchange: semantics and query answering. Theoretical Computer Science 336(1), 89–124 (2005). https://doi.org/10.1016/j.tcs.2004.10.033, database Theory
Feller, T., Lyon, T.S., Ostropolski-Nalewaja, P., Rudolph, S.: Finite-Cliquewidth Sets of Existential Rules: Toward a General Criterion for Decidable yet Highly Expressive Querying. In: Geerts, F., Vandevoort, B. (eds.) 26th International Conference on Database Theory (ICDT 2023). Leibniz International Proceedings in Informatics (LIPIcs), vol. 255, pp. 18:1–18:18. Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl, Germany (2023). https://doi.org/10.4230/LIPIcs.ICDT.2023.18
Johnson, D.S., Klug, A.: Testing containment of conjunctive queries under functional and inclusion dependencies. In: Proceedings of the 1st ACM SIGACT-SIGMOD Symposium on Principles of Database Systems. p. 164–169. PODS ’82, Association for Computing Machinery, New York, NY, USA (1982). https://doi.org/10.1145/588111.588138
Lyon, T.S., Rudolph, S.: Derivation-graph-based characterizations of decidable existential rule sets. CoRR (2023). https://doi.org/10.48550/arXiv.2307.08481
Maier, D., Mendelzon, A.O., Sagiv, Y.: Testing implications of data dependencies. ACM Trans. Database Syst. 4(4), 455–469 (December 1979). https://doi.org/10.1145/320107.320115
Thomazo, M., Baget, J.F., Mugnier, M.L., Rudolph, S.: A generic querying algorithm for greedy sets of existential rules. In: Brewka, G., Eiter, T., McIlraith, S.A. (eds.) Proceedings of the 13th International Conference on Principles of Knowledge Representation and Reasoning (KR’12). AAAI (2012), http://www.aaai.org/ocs/index.php/KR/KR12/paper/view/4542
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Lyon, T.S., Rudolph, S. (2023). Derivation-Graph-Based Characterizations of Decidable Existential Rule Sets. In: Gaggl, S., Martinez, M.V., Ortiz, M. (eds) Logics in Artificial Intelligence. JELIA 2023. Lecture Notes in Computer Science(), vol 14281. Springer, Cham. https://doi.org/10.1007/978-3-031-43619-2_26
Download citation
DOI: https://doi.org/10.1007/978-3-031-43619-2_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-43618-5
Online ISBN: 978-3-031-43619-2
eBook Packages: Computer ScienceComputer Science (R0)