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## Conjunctive Queries with Negation over DL-Lite: A Closer Look

Citations: | 3 - 2 self |

### Citations

473 | Tractable reasoning and efficient query answering in description logics: the DL-Lite family.
- Calvanese, Giacomo, et al.
- 2007
(Show Context)
Citation Context ... of data, in particular, by delegating query evaluation to relational database management systems. Among the different proposed DLs fulfilling these requirements we find members of the DL-Lite family =-=[1, 2]-=-, which form the basis of OWL 2 QL, one of the three profiles of the Web Ontology Language OWL 2, and where answering (unions of) CQs is in AC 0 in data complexity. In recent years, the problem of ans... |

195 | The DL-lite family and relations.
- Artale, Calvanese, et al.
- 2009
(Show Context)
Citation Context ... of data, in particular, by delegating query evaluation to relational database management systems. Among the different proposed DLs fulfilling these requirements we find members of the DL-Lite family =-=[1, 2]-=-, which form the basis of OWL 2 QL, one of the three profiles of the Web Ontology Language OWL 2, and where answering (unions of) CQs is in AC 0 in data complexity. In recent years, the problem of ans... |

107 | The complexity of relational query languages (extended abstract
- Vardi
- 1982
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Citation Context ...d write K |= q(c) if c is an answer to q in all models of K. In OBDA scenarios the size of the query and the TBox is much smaller than the size of the ABox. This is why we explore the data complexity =-=[10]-=- of the query answeringproblem, that is, we assume that only the ABox is considered as part of the input. Formally, let T be a DL-Lite H core or DL-Litecore TBox and q(x) a (U)CQ ¬s or a (U)CQ = . W... |

82 | J.B.: The chase revisited
- Deutsch, Nash, et al.
- 2008
(Show Context)
Citation Context ...fficult to show undecidability using encodings similar to those for unions of CQs = and CQs ¬s . Second, in contrast to positive atoms of CQs, the negated atoms are not preserved under homomorphisms =-=[7]-=-, hence query answering techniques based on the canonical model construction [1, 8] cannot be directly applied. In fact, up to now, the only known result is CONP-hardness for CQs = and CQs ¬s over DL... |

62 | The combined approach to query answering in DL-Lite.
- Kontchakov, Lutz, et al.
- 2010
(Show Context)
Citation Context ...s = and CQs ¬s . Second, in contrast to positive atoms of CQs, the negated atoms are not preserved under homomorphisms [7], hence query answering techniques based on the canonical model construction =-=[1, 8]-=- cannot be directly applied. In fact, up to now, the only known result is CONP-hardness for CQs = and CQs ¬s over DL-Litecore [3, 5]; Gutiérrez-Basulto et al. [5] claimed a matching upper bound for C... |

24 | The limits of querying ontologies
- Rosati
(Show Context)
Citation Context ... in data complexity. In recent years, the problem of answering more expressive queries over DL-Lite has been investigated [3–6]; in particular, following the tradition of relational databases, Rosati =-=[3]-=- and Gutiérrez-Basulto et al. [5] investigated extensions of CQs with two restricted forms of negated atoms: (1) inequality (CQ = ) and (2) safe negation (CQ ¬s ). It is well-known in databases and o... |

7 | Answering expressive path queries over lightweight DL knowledge bases
- Bienvenu, Ortiz, et al.
- 2012
(Show Context)
Citation Context ...y, u), (1) Hq(x) ∧ Ca(x) ∧ S(x, y) ∧ T σ (y, z) → Pq ′ a ′(y, z), for δ(q, a) = (q′ , a ′ , σ), (2) H ∅(x) ∧ Ca(x) ∧ S(x, y) → Ca(y), for a ∈ Γ, (3) Dσ(y) ∧ T σ (y, z) → T ∅σ(y, z), for σ ∈ {−1, +1}, =-=(4)-=- T0(x, y) → T (x, y), (5) where T σ (y, z) stands for T (y, z) if σ = +1 and T (z, y) if σ = −1, and a TBox T containing the following concept inclusions: ∃T ⊑ ∃S, ∃T − 0 ⊑ ∃T0 ⊓ C , (6) ∃P − qa ⊑ Hq,... |

7 | Answering counting aggregate queries over ontologies of the DL-Lite family. In:
- Kostylev, Reutter
- 2013
(Show Context)
Citation Context ...σ ∈ {−1, +1}, (4) T0(x, y) → T (x, y), (5) where T σ (y, z) stands for T (y, z) if σ = +1 and T (z, y) if σ = −1, and a TBox T containing the following concept inclusions: ∃T ⊑ ∃S, ∃T − 0 ⊑ ∃T0 ⊓ C , =-=(6)-=- ∃P − qa ⊑ Hq, ∃Pqa ⊑ Ca, for q ∈ Q and a ∈ Γ, (7) Hq ⊑ Dσ, ∃T − ∅σ ⊑ Dσ ⊓ H ∅, for q ∈ Q and σ ∈ {−1, +1}, (8) Hq1 ⊑ ⊥. (9) For every input w = a1 . . . an ∈ Γ ∗ , we take the following ABox Aw: Hq0 ... |

5 |
R.: An update on query answering with restricted forms of negation
- Gutiérrez-Basulto, Ibáñez-Garcı́a, et al.
- 2012
(Show Context)
Citation Context ...ars, the problem of answering more expressive queries over DL-Lite has been investigated [3–6]; in particular, following the tradition of relational databases, Rosati [3] and Gutiérrez-Basulto et al. =-=[5]-=- investigated extensions of CQs with two restricted forms of negated atoms: (1) inequality (CQ = ) and (2) safe negation (CQ ¬s ). It is well-known in databases and other areas related to management ... |

3 |
Über die Entscheidbarkeit von konjunktiv Anfragen mit Ungleichheit in der Beschreibungslogik EL
- Klenke
- 2010
(Show Context)
Citation Context ... with a single inequality (a proof along the lines of Section 3 would require many inequalities). We mention in passing that CQ = answering over light-weight description logic EL is also undecidable =-=[9]-=-; however, CQ answering in EL is P-complete rather than in AC 0 (in data complexity). In the second part of the paper, we consider the problem of answering CQs = over DL-Litecore, the language withou... |

2 |
Computational complexity. Academic Internet Publ
- Papadimitriou
- 2007
(Show Context)
Citation Context ...ERS (q, T ) is P-hard. Proof. The proof is by reduction of the complement of HORN-3SAT, the satisfiability problem for Horn clauses with at most 3 literals, which is known to be P-complete (see e.g., =-=[11]-=-). Suppose we are given a conjunction ψ of clauses of the form p, ¬p, and p1 ∧ p2 → p. Fix a TBox T containing the following concept inclusions: VT ⊓ VF ⊑ ⊥, G ⊑ ∃T, ∃T − ⊑ ∃T, ∃T − ⊑ VT , and a Boole... |