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Finite-Cliquewidth Sets of Existential Rules: Toward a General Criterion for Decidable yet Highly Expressive Querying

Authors Thomas Feller , Tim S. Lyon , Piotr Ostropolski-Nalewaja , Sebastian Rudolph

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Author Details

Thomas Feller
  • Technische Universität Dresden, Germany
Tim S. Lyon
  • Technische Universität Dresden, Germany
Piotr Ostropolski-Nalewaja
  • Technische Universität Dresden, Germany
  • University of Wrocław, Poland
Sebastian Rudolph
  • Technische Universität Dresden, Germany

Funding

Work supported by the European Research Council (ERC) Consolidator Grant 771779 A Grand Unified Theory of Decidability in Logic-Based Knowledge Representation (DeciGUT).

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Thomas Feller, Tim S. Lyon, Piotr Ostropolski-Nalewaja, and Sebastian Rudolph. Finite-Cliquewidth Sets of Existential Rules: Toward a General Criterion for Decidable yet Highly Expressive Querying. In 26th International Conference on Database Theory (ICDT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 255, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ICDT.2023.18

Abstract

In our pursuit of generic criteria for decidable ontology-based querying, we introduce finite-cliquewidth sets (fcs) of existential rules, a model-theoretically defined class of rule sets, inspired by the cliquewidth measure from graph theory. By a generic argument, we show that fcs ensures decidability of entailment for a sizable class of queries (dubbed DaMSOQs) subsuming conjunctive queries (CQs). The fcs class properly generalizes the class of finite-expansion sets (fes), and for signatures of arity ≤ 2, the class of bounded-treewidth sets (bts). For higher arities, bts is only indirectly subsumed by fcs by means of reification. Despite the generality of fcs, we provide a rule set with decidable CQ entailment (by virtue of first-order-rewritability) that falls outside fcs, thus demonstrating the incomparability of fcs and the class of finite-unification sets (fus). In spite of this, we show that if we restrict ourselves to single-headed rule sets over signatures of arity ≤ 2, then fcs subsumes fus.

Subject Classification

ACM Subject Classification
  • Theory of computation → Description logics
  • Theory of computation → Database query languages (principles)
  • Theory of computation → Logic and databases
  • Mathematics of computing → Graph theory
Keywords
  • existential rules
  • TGDs
  • cliquewidth
  • treewidth
  • bounded-treewidth sets
  • finite-unification sets
  • first-order rewritability
  • monadic second-order logic
  • datalog

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