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## On the succinctness of query rewriting over OWL 2 QL ontologies with shallow chases (2014)

Citations: | 3 - 3 self |

### Citations

1836 |
V.: Foundations of Databases
- Abiteboul, Hull, et al.
- 1995
(Show Context)
Citation Context ... have (T ,A) |= q(~a) iff A |= q′(~a).2 If q′ is a positive existential formula, we call it a PE-rewriting of q and T . We also consider rewritings in the form of nonrecursive datalog queries. Recall =-=[1]-=- that a datalog program, Π, is a finite set of Horn clauses ∀~x (γ1 ∧ · · · ∧ γm → γ0), where each γi is an atom of the form P (x1, . . . , xl) with xi ∈ ~x. The atom γ0 is the head of the clause, and... |

468 | Tractable Reasoning and Efficient Query Answering in Description Logics: The DL-Lite Family
- Calvanese, Giacomo, et al.
- 2007
(Show Context)
Citation Context ...ta sources and enriching the data with additional knowledge. OBDA is widely regarded as a key to the new generation of information systems. OWL2QL is based on the DL-Lite family of description logics =-=[11, 4]-=-; other languages supporting FOrewritability of CQs include linear, sticky and sticky-join sets of tuple-generating dependencies [10, 7]. In practice, rewriting-based OBDA systems1 can only work effic... |

354 |
Y.: The Classical Decision Problem
- Börger, Grädel, et al.
- 1997
(Show Context)
Citation Context ... 2 with hyperedges e1, . . . , ek. We first provide a graph-theoretic characterisation of independent sets covering all zeros based on the implication graph [5] (or the chain criterion of Lemma 8.3.1 =-=[9]-=-). With any hyperedge ei we associate a propositional variable pei and with an input ~α we associate the following set Φ~α of binary clauses: – ¬pei ∨¬pej , if ei ∩ ej 6= ∅ (informally: intersecting h... |

347 | Computational Complexity: A Modern Approach
- Arora, Barak
- 2009
(Show Context)
Citation Context ...ses. 3 Hypergraph Functions The rewriting qtw gives rise to monotone Boolean functions we call hypergraph functions. For the complexity theory of monotone Boolean functions, the reader is referred to =-=[3, 18]-=-. Let H = (V,E) be a hypergraph with vertices v ∈ V and hyperedges e ∈ E, E ⊆ 2V . A subset X ⊆ E is independent if e ∩ e′ = ∅, for any distinct e, e′ ∈ X . Denote by VX the set of vertices occurring ... |

201 |
A linear-time algorithm for testing the truth of certain quantified boolean formulas
- Aspvall, Plass, et al.
- 1979
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Citation Context ...omputed by a hypergraph program H of degree 2 with hyperedges e1, . . . , ek. We first provide a graph-theoretic characterisation of independent sets covering all zeros based on the implication graph =-=[5]-=- (or the chain criterion of Lemma 8.3.1 [9]). With any hyperedge ei we associate a propositional variable pei and with an input ~α we associate the following set Φ~α of binary clauses: – ¬pei ∨¬pej , ... |

192 | M.: The DL-Lite family and relations
- Artale, Calvanese, et al.
- 2009
(Show Context)
Citation Context ...ta sources and enriching the data with additional knowledge. OBDA is widely regarded as a key to the new generation of information systems. OWL2QL is based on the DL-Lite family of description logics =-=[11, 4]-=-; other languages supporting FOrewritability of CQs include linear, sticky and sticky-join sets of tuple-generating dependencies [10, 7]. In practice, rewriting-based OBDA systems1 can only work effic... |

164 |
Monotone circuits for connectivity require super-logarithmic depth
- Karchmer, Wigderson
- 1988
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Citation Context ...g Boolean functions as hypergraphs of degree 2 is polynomially equivalent to representing their duals as nondeterministic branching programs (NBPs) [18]. This correspondence and known results on NBPs =-=[31, 19]-=- give (i), (ii) and (iv) above. To prove (v), we observe that hypergraphs of degree 3 are computationally as powerful as nondeterministic Boolean circuits (NP/poly) and encode the function CLIQUEn,k(~... |

140 | The monotone circuit complexity of boolean functions
- Alon, Boppana
- 1987
(Show Context)
Citation Context ...ejj′ = 1} contains a k-clique. A series of papers, started by Razborov’s [30], gave an exponential lower bound for the size of monotone circuits computing CLIQUEn,k: 2Ω( √ k) for k ≤ 14 (n/ log n)2/3 =-=[2]-=-. For monotone formulas, an even better lower bound is known: 2Ω(k) for k = 2n/3 [29]. 12 We first construct a monotone HGP computing CLIQUEn,k and then use the intuition behind the construction to en... |

115 | A.: Conjunctive query containment revisited
- Chekuri, Rajaraman
- 2000
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Citation Context ...nce CLIQUEn,k is NP/poly-complete under NC 1 reductions, this gives us NP/poly ⊆ NC1. q 7 Rewritings of Tree-Shaped CQs A CQ is said to be tree-shaped if its Gaifman graph is a tree. It is well known =-=[35, 12]-=- that tree-shaped CQs (or, more generally, CQs of bounded treewidth) can be evaluated over plain data instances in polynomial time. In contrast, the evaluation of arbitrary CQs is NP-complete for comb... |

62 |
Boolean Function Complexity: Advances and Frontiers
- Jukna
- 2012
(Show Context)
Citation Context ...hypergraph function for H . We show that representing Boolean functions as hypergraphs of degree 2 is polynomially equivalent to representing their duals as nondeterministic branching programs (NBPs) =-=[18]-=-. This correspondence and known results on NBPs [31, 19] give (i), (ii) and (iv) above. To prove (v), we observe that hypergraphs of degree 3 are computationally as powerful as nondeterministic Boolea... |

58 | A.: Ontological queries: Rewriting and optimization
- Gottlob, Orsi, et al.
- 2011
(Show Context)
Citation Context ... and superpolynomial FO-rewritings (unless NP ⊆ P/poly); [20] also showed that NDL-rewritings 1See, e.g., QuOnto [28], Presto/Prexto [34, 33], Rapid [13], Ontop [32], Requiem/Blackout [26, 27], Nyaya =-=[15]-=-, Clipper [14] and [23]. 1 (FO-rewritings) can be exponentially (superpolynomially) more succinct than PE-rewritings. These prohibitively high lower bounds are caused by the fact that the chases (cano... |

38 |
Extending Decidable Cases for Rules with Existential Variables
- Baget, Leclère, et al.
- 2009
(Show Context)
Citation Context ...ms. OWL2QL is based on the DL-Lite family of description logics [11, 4]; other languages supporting FOrewritability of CQs include linear, sticky and sticky-join sets of tuple-generating dependencies =-=[10, 7]-=-. In practice, rewriting-based OBDA systems1 can only work efficiently with those CQs and ontologies that have reasonably short rewritings. This obvious fact raises fundamental succinctness problems s... |

33 | Rewriting Ontological Queries into Small Nonrecursive Datalog Programs
- Gottlob, Schwentick
- 2012
(Show Context)
Citation Context ... tree-shaped Boolean CQs and any T , is fixedparameter tractable (recall that the problem ‘A |= q?’, for tree-shaped q, is known to be tractable [35], while ‘T ,A |= q?’ is NP-hard [21]). As shown in =-=[16]-=-, exponential rewritings can be made polynomial at the expense of polynomially-many additional existential quantifiers over a domain with two constants not necessarily occurring in the CQs; cf. [6]. I... |

23 |
A.: Towards more expressive ontology languages: The query answering problem
- Cal̀ı, Gottlob, et al.
- 2012
(Show Context)
Citation Context ...ms. OWL2QL is based on the DL-Lite family of description logics [11, 4]; other languages supporting FOrewritability of CQs include linear, sticky and sticky-join sets of tuple-generating dependencies =-=[10, 7]-=-. In practice, rewriting-based OBDA systems1 can only work efficiently with those CQs and ontologies that have reasonably short rewritings. This obvious fact raises fundamental succinctness problems s... |

23 | Optimized Query Rewriting for OWL 2 QL
- Chortaras, Trivela, et al.
- 2011
(Show Context)
Citation Context ...ial (PE) and nonrecursive datalog (NDL) rewritings, and superpolynomial FO-rewritings (unless NP ⊆ P/poly); [20] also showed that NDL-rewritings 1See, e.g., QuOnto [28], Presto/Prexto [34, 33], Rapid =-=[13]-=-, Ontop [32], Requiem/Blackout [26, 27], Nyaya [15], Clipper [14] and [23]. 1 (FO-rewritings) can be exponentially (superpolynomially) more succinct than PE-rewritings. These prohibitively high lower ... |

21 |
Eliminating definitions and Skolem functions in first-order logic
- Avigad
(Show Context)
Citation Context ...n [16], exponential rewritings can be made polynomial at the expense of polynomially-many additional existential quantifiers over a domain with two constants not necessarily occurring in the CQs; cf. =-=[6]-=-. Intuitively, given q, T and A, the extra quantifiers guess a homomorphism from q to the chase for (T ,A), whereas the standard rewritings (without extra constants) represent such homomorphisms expli... |

19 | Query rewriting for Horn-SHIQ plus rules
- Eiter, Ortiz, et al.
- 2012
(Show Context)
Citation Context ...nomial FO-rewritings (unless NP ⊆ P/poly); [20] also showed that NDL-rewritings 1See, e.g., QuOnto [28], Presto/Prexto [34, 33], Rapid [13], Ontop [32], Requiem/Blackout [26, 27], Nyaya [15], Clipper =-=[14]-=- and [23]. 1 (FO-rewritings) can be exponentially (superpolynomially) more succinct than PE-rewritings. These prohibitively high lower bounds are caused by the fact that the chases (canonical models) ... |

19 | The combined approach to OBDA: Taming role hierarchies using filters
- Lutz, Seylan, et al.
- 2012
(Show Context)
Citation Context ...As are exponentially more succinct than DFAs, and ∃-QBFs are exponentially more succinct than SAT). A more practical utilisation of additional constants was suggested in the combined approach to OBDA =-=[24]-=-, where they are used to construct a polynomial-size encoding of the chase for the given ontology and data over which the original CQ is evaluated. This encoding may introduce (exponentially-many in t... |

16 | On (In)Tractability of OBDA with OWL 2 QL
- Kikot, Kontchakov, et al.
- 2011
(Show Context)
Citation Context ...m ‘T ,A |= q?’, for tree-shaped Boolean CQs and any T , is fixedparameter tractable (recall that the problem ‘A |= q?’, for tree-shaped q, is known to be tractable [35], while ‘T ,A |= q?’ is NP-hard =-=[21]-=-). As shown in [16], exponential rewritings can be made polynomial at the expense of polynomially-many additional existential quantifiers over a domain with two constants not necessarily occurring in ... |

16 | Conjunctive query answering with OWL 2 QL
- Kikot, Kontchakov, et al.
- 2012
(Show Context)
Citation Context ...ulas, monotone formulas and monotone circuits computing certain monotone Boolean functions, on the other. These functions are associated with hypergraph representations of the tree-witness rewritings =-=[22]-=-, reflecting possible homomorphisms of the given CQ to the labelled nulls of the chases for the given ontology. In particular, any hypergraph H of degree 2 (every vertex in which belongs to 2 hyperedg... |

14 | Exponential lower bounds and separation for query rewriting
- Kikot, Kontchakov, et al.
(Show Context)
Citation Context ...worst case? Can rewritings of one type (say, nonrecursive datalog) be substantially shorter than rewritings of another type (say, positive existential)? First answers to these questions were given in =-=[20]-=- which constructed CQs qn and ontologies Tn, n < ω, with only exponential positive existential (PE) and nonrecursive datalog (NDL) rewritings, and superpolynomial FO-rewritings (unless NP ⊆ P/poly); [... |

13 | Monotone separation of logarithmic space from logarithmic depth
- Grigni, Sipser
- 1995
(Show Context)
Citation Context ...ormulas computing fn are of size nΩ(logn). In fact, fn from [19] checks whether two given vertices are connected by a path in a given undirected graph (alternatively, one could use the functions from =-=[17]-=-). By Theorem 8 (ii) and Lemma 7, there is a sequence of polynomial-size monotone HGPs H ′n of degree 2 computing f∗n. By applying Theorem 13 to the hypergraph Hn of H ′ n, we obtain a sequence of CQs... |

11 | Tractable queries for lightweight description logics
- Bienvenu, Ortiz, et al.
(Show Context)
Citation Context ...ped CQ q(~x) = ∃~y ϕ(~x, ~y), we pick some variable as its root and define a partial order on the variables of q by taking z z′ iff z′ occurs in the subtree of q rooted in z. The strategy used in =-=[8]-=- chooses the smallest z with respect to. Since the number of distinct subtrees of q is bounded by |q| and NDL programs allow for structure sharing, this strategy yields an NDL-rewriting of size |T | ... |

6 |
On the exploration of the query rewriting space with existential rules
- König, Leclère, et al.
- 2013
(Show Context)
Citation Context ...-rewritings (unless NP ⊆ P/poly); [20] also showed that NDL-rewritings 1See, e.g., QuOnto [28], Presto/Prexto [34, 33], Rapid [13], Ontop [32], Requiem/Blackout [26, 27], Nyaya [15], Clipper [14] and =-=[23]-=-. 1 (FO-rewritings) can be exponentially (superpolynomially) more succinct than PE-rewritings. These prohibitively high lower bounds are caused by the fact that the chases (canonical models) for Tn co... |