## Query Rewriting under Non-Guarded Rules

Citations: | 4 - 3 self |

### BibTeX

@MISC{Calì_queryrewriting,

author = {Andrea Calì and Georg Gottlob and Andreas Pieris},

title = {Query Rewriting under Non-Guarded Rules},

year = {}

}

### OpenURL

### Abstract

Abstract. We address the problem of answering conjunctive queries over knowledge bases, specified by sets of first-order sentences called tuple-generating dependencies (TGDs). This problem is highly relevant to query optimization, information integration, and ontological reasoning. We present a rewriting algorithm, inspired by resolution in Logic Programming, which is capable of dealing with an expressive class of TGDs, called sticky TGDs. Given a set of sticky TGDs and a conjunctive query, the algorithm produces a first-order query that can be then evaluated over the data, providing the correct answers. In this way, we establish that conjunctive query answering under sticky TGDs is in the highly tractable class ac0 in the data complexity. 1

### Citations

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Citation Context ...ng technique are given. We recall that ac0 is the complexity class of recognizing words in languages defined by constant-depth Boolean circuits with an (unlimited fan-in) and and or gates (see, e.g., =-=[20]-=-). Notice that a UCQs can be immediately translated into an SQL query, therefore the rewriting algorithm is especially suitable for real-world applications based on relational DBMSs. Notice that the s... |

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Citation Context ...s Entity-Relationship schemas, and [23] deals with expressive constraints based on Answer Set Programming. [6] introduces and studies first-order constraints derived from a “light” version of F-logic =-=[18]-=-, called F-logic Lite. Another relevant formalisms for knowledge bases, especially in the Semantic Web, is the DL-lite family; in [10, 22] tractable query answering techniques under DL-lite knowledge ... |

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Citation Context ...vice discovery (see, e.g., [11]). In the database field, the problem of answering queries on incomplete data under constraints (a.k.a. dependencies) is tightly related to the one of query containment =-=[12]-=-; in fact, the two problems are mutually reducible (see, e.g., [3]). A milestone paper in the field is [17]; it addresses conjunctive query containment under functional and inclusion dependencies, a c... |

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Citation Context ... Several works have recently studied query evaluation problems for settings where the chase terminates and thus generates a finite solution. This is the typical setting, for example, of data exchange =-=[15]-=-, where the materialization (and therefore the finiteness) of the chase is a requirement. To this aim, syntactic restrictions on TGDs, e.g., weak acyclicity [13], have been proposed. Little was known ... |

317 | Tractable reasoning and efficient query answering in description logics: The DL-Lite family
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(Show Context)
Citation Context ...first-order constraints derived from a “light” version of F-logic [18], called F-logic Lite. Another relevant formalisms for knowledge bases, especially in the Semantic Web, is the DL-lite family; in =-=[10, 22]-=- tractable query answering techniques under DL-lite knowledge bases are presented. A more general approach is adopted in the recent papers [3, 4]; in such works, instead of focusing on a specific logi... |

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Citation Context ...first-order constraints derived from a “light” version of F-logic [18], called F-logic Lite. Another relevant formalisms for knowledge bases, especially in the Semantic Web, is the DL-lite family; in =-=[10, 22]-=- tractable query answering techniques under DL-lite knowledge bases are presented. A more general approach is adopted in the recent papers [3, 4]; in such works, instead of focusing on a specific logi... |

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Citation Context ...is [17]; it addresses conjunctive query containment under functional and inclusion dependencies, a class of constraints that is highly relevant in practice. The results of [17] were later extended in =-=[7]-=-. Other works consider different classes of constraints. For instance, [2, 9] consider constraints tailored to express Entity-Relationship schemas, and [23] deals with expressive constraints based on ... |

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Citation Context ... large part of the aforementioned works on query answering and containment are based on the well-known notion of chase, widely used for dependency implication and query containment under dependencies =-=[19, 17]-=-. The chase is a procedure that enforces the satisfaction of TGDs by the addition of suitable tuples. For example, consider an instance D consisting of the atoms {director(d),leads(d,g)}; the above TG... |

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Citation Context ...a under constraints (a.k.a. dependencies) is tightly related to the one of query containment [12]; in fact, the two problems are mutually reducible (see, e.g., [3]). A milestone paper in the field is =-=[17]-=-; it addresses conjunctive query containment under functional and inclusion dependencies, a class of constraints that is highly relevant in practice. The results of [17] were later extended in [7]. Ot... |

77 |
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Citation Context ...s in C, and for every BCQ q, there exists a first-order query qΣ such that, for every database D, D ∪Σ |= q iff D |= qΣ [4]. Since answering first-order queries is in the class ac0 in data complexity =-=[24]-=-, it immediately follows that for FO-rewritable TGDs, query answering is in ac0 in data complexity. In this section we establish that STGDs are FO-rewritable by providing a query rewriting algorithm, ... |

74 | Query rewriting and answering under constraints in data integration systems
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(Show Context)
Citation Context ...n the data, returns the correct answers. We consider the class of conjunctive queries (CQs), also called select-project-join queries in the database literature. The algorithm, inspired by the ones in =-=[2, 8]-=-, takes as inputa set of STGDs and a conjunctive query, and it computes a (finite) rewriting expressed in union of conjunctive queries (UCQs). Since our rewriting algorithm is sound and complete (est... |

71 | A general datalog-based framework for tractable query answering over ontologies
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(Show Context)
Citation Context ... rewritable, henceforth abbreviated as FO-rewritable, iff for every set Σ of TGDs in C, and for every BCQ q, there exists a first-order query qΣ such that, for every database D, D ∪Σ |= q iff D |= qΣ =-=[4]-=-. Since answering first-order queries is in the class ac0 in data complexity [24], it immediately follows that for FO-rewritable TGDs, query answering is in ac0 in data complexity. In this section we ... |

55 | Taming the infinite chase: Query answering under expressive relational constraints
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(Show Context)
Citation Context ...m of answering queries on incomplete data under constraints (a.k.a. dependencies) is tightly related to the one of query containment [12]; in fact, the two problems are mutually reducible (see, e.g., =-=[3]-=-). A milestone paper in the field is [17]; it addresses conjunctive query containment under functional and inclusion dependencies, a class of constraints that is highly relevant in practice. The resul... |

52 |
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(Show Context)
Citation Context ...the set {t | t ∈ q(B) for each B ∈ mods(D,Σ)}. The answer to a BCQ q w.r.t. D and Σ is positive, denoted as D ∪Σ |= q, iff ans(q,D,Σ) ̸= ∅. Note that query answering under general TGDs is undecidable =-=[1]-=-, even when the schema and the set of TGDs are fixed [3]. We recall that the two problems of CQ and BCQ evaluation under TGDs are logspace-equivalent [3]. Moreover, it is easy to see that the query ou... |

31 | Conjunctive query containment and answering under description logics constraints
- Calvanese, Giacomo, et al.
- 2008
(Show Context)
Citation Context ...ion Answering queries over knowledge bases is a fundamental problem in knowledge representation. It has been employed in schema integration, information integration, and service discovery (see, e.g., =-=[11]-=-). In the database field, the problem of answering queries on incomplete data under constraints (a.k.a. dependencies) is tightly related to the one of query containment [12]; in fact, the two problems... |

25 | Accessing data integration systems through conceptual schemas
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(Show Context)
Citation Context ...nclusion dependencies, a class of constraints that is highly relevant in practice. The results of [17] were later extended in [7]. Other works consider different classes of constraints. For instance, =-=[2, 9]-=- consider constraints tailored to express Entity-Relationship schemas, and [23] deals with expressive constraints based on Answer Set Programming. [6] introduces and studies first-order constraints de... |

13 | Containment of conjunctive object meta-queries - Calı̀, Kifer - 2006 |

12 |
XML query reformulation over mixed and redundant storage
- Deutsch
(Show Context)
Citation Context ...setting, for example, of data exchange [15], where the materialization (and therefore the finiteness) of the chase is a requirement. To this aim, syntactic restrictions on TGDs, e.g., weak acyclicity =-=[13]-=-, have been proposed. Little was known about the cases where the chase is (in general) infinite, with the notable exception of the classical work of Johnson and Klug [17]. In this work, along the line... |

8 |
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(Show Context)
Citation Context ...s(z2),...}. It is well-known that the (possibly infinite) chase for D and Σ is a universal model of D w.r.t. Σ, i.e., for each database B ∈ mods(D,Σ), there exists a homomorphism from chase(D,Σ) to B =-=[15, 14]-=-. Using this fact it can be shown that for a BCQ q, D ∪ Σ |= q iff chase(D,Σ) |= q. 3 Sticky TGDs In this section we recall the class of sticky TGDs introduced in [5]. As we shall see, query answering... |

8 | Decidability issues for action guarded logics
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(Show Context)
Citation Context ...d extends a large class of knowledge representation formalisms in the literature, in particularthe DL-lite family. The constraints of [3, 4] are inspired by the guarded fragment of first-order logic =-=[16]-=-, and among them are the languages of linear Datalog ± , guarded Datalog ± , and weakly-guarded Datalog ± . It is important to notice that Datalog ± -rules are relevant tuple-generating dependencies (... |

8 | DNC: Decidable Non-monotonic Disjunctive Logic Programs with Function Symbols
- Simkus, Eiter
- 2007
(Show Context)
Citation Context .... The results of [17] were later extended in [7]. Other works consider different classes of constraints. For instance, [2, 9] consider constraints tailored to express Entity-Relationship schemas, and =-=[23]-=- deals with expressive constraints based on Answer Set Programming. [6] introduces and studies first-order constraints derived from a “light” version of F-logic [18], called F-logic Lite. Another rele... |

2 |
Querying incomplete data over extended er schemata
- Calì, Martinenghi
- 2010
(Show Context)
Citation Context ...nclusion dependencies, a class of constraints that is highly relevant in practice. The results of [17] were later extended in [7]. Other works consider different classes of constraints. For instance, =-=[2, 9]-=- consider constraints tailored to express Entity-Relationship schemas, and [23] deals with expressive constraints based on Answer Set Programming. [6] introduces and studies first-order constraints de... |

2 | Practical aspects of query rewriting for OWL2
- Pérez-Urbina, Horrocks, et al.
(Show Context)
Citation Context ...e in data complexity, this leaves space for further optimizations. Generating “smaller” rewritings is one of the directions currently pursued to improve efficiency of query processing in this context =-=[21]-=-. In [5] it is shown, similarly to what is done in [4], that STGDs enriched with negative constraints of the form ∀Xϕ(X) → ⊥, where ϕ(X) is a conjunction of atoms and ⊥ is the constant false, and with... |

1 |
Advanced processing for ontological query answering
- Calì, Gottlob, et al.
- 2010
(Show Context)
Citation Context ...ical work of Johnson and Klug [17]. In this work, along the lines of [3, 4], we also adopt a general approach. We consider an expressive class of TGDs, called sticky TGDs (STGDs), first introduced in =-=[5]-=- as an addition to the Datalog ± family. The chase under STGDs is not guaranteed to terminate. Stickiness is formally defined in Section 3 by an efficiently testable condition involving variable-marki... |