On the first-order expressibility of computing certain answers to conjunctive queries over uncertain databases

2010 ◽  
Author(s):  
Jef Wijsen
Keyword(s):  
Uncertain Databases ◽  
Conjunctive Queries ◽  
First Order ◽  
Certain Answers

scholarly journals Best Answers over Incomplete Data : Complexity and First-Order Rewritings

2019 ◽  
Author(s):  
Amélie Gheerbrant ◽  
Cristina Sirangelo
Keyword(s):  
Incomplete Data ◽  
Decision Problem ◽  
Possible Worlds ◽  
Query Answering ◽  
Query Rewriting ◽  
Conjunctive Queries ◽  
First Order ◽  
Database Technology ◽  
Practical Algorithm ◽  
Certain Answers

Answering queries over incomplete data is ubiquitous in data management and in many AI applications that use query rewriting to take advantage of relational database technology. In these scenarios one lacks full information on the data but queries still need to be answered with certainty. The certainty aspect often makes query answering unfeasible except for restricted classes, such as unions of conjunctive queries. In addition often there are no, or very few certain answers, thus expensive computation is in vain. Therefore we study a relaxation of certain answers called best answers. They are defined as those answers for which there is no better one (that is, no answer true in more possible worlds). When certain answers exist the two notions coincide. We compare different ways of casting query answering as a decision problem and characterise its complexity for first-order queries, showing significant differences in the behavior of best and certain answers.We then restrict attention to best answers for unions of conjunctive queries and produce a practical algorithm for finding them based on query rewriting techniques.

scholarly journals VERIFICATION OF CONJUNCTIVE ARTIFACT-CENTRIC SERVICES

2012 ◽  
Vol 21 (02) ◽  
pp. 111-139 ◽  
Author(s):  
GIUSEPPE DE GIACOMO ◽  
RICCARDO DE MASELLIS ◽  
RICCARDO ROSATI
Keyword(s):  
Relational Database ◽  
Data Exchange ◽  
Recent Literature ◽  
Conjunctive Queries ◽  
First Order ◽  
Temporal Properties ◽  
Verification Time

An artifact-centric service is a stateful service that holistically represents both the data and the process in terms of a (dynamic) artifact. An artifact is constituted by a data component, holding all the data of interest for the service, and a lifecycle, which specifies the process that the service enacts. In this paper, we study artifact-centric services whose data component is a full-fledged relational database, queried through (first-order) conjunctive queries, and the lifecycle component is specified as sets of condition-action rules, where actions are tasks invocations, again based on conjunctive queries. Notably, the database can evolve in an unbounded way due to new values (unknown at verification time) inserted by tasks. The main result of the paper is that verification in this setting is decidable under a reasonable restriction on the form of tasks, called weak acyclicity, which we borrow from the recent literature on data exchange. In particular, we develop a sound, complete and terminating verification procedure for sophisticated temporal properties expressed in a first-order variant of μ-calculus.

scholarly journals Relaxing and Restraining Queries for OBDA

2019 ◽  
Vol 33 ◽  
pp. 2654-2661
Author(s):  
Medina Andreşel ◽  
Yazmín Ibáñez-García ◽  
Magdalena Ortiz ◽  
Mantas Šimkus
Keyword(s):  
Data Models ◽  
Conjunctive Queries ◽  
First Order ◽  
Rewriting Rules ◽  
Representation Of Knowledge

We advocate the use of ontologies for relaxing and restraining queries, so that they retrieve either more or less answers, enabling the exploration of a given dataset. We propose a set of rewriting rules to relax and restrain conjunctive queries (CQs) over datasets mediated by an ontology written in a dialect of DL-Lite with complex role inclusions (CRIs). The addition of CRI enables the representation of knowledge about data involving ordered hierarchies of categories, in the style of multi-dimensional data models. Although CRIs in general destroy the first-order rewritability of CQs, we identify settings in which CQs remain rewritable.

scholarly journals Parameterised Queries and Lifted Query Answering

2018 ◽  
Author(s):  
Tanya Braun ◽  
Ralf Möller
Keyword(s):  
Random Variables ◽  
Query Answering ◽  
Standard Approach ◽  
Tree Algorithm ◽  
Conjunctive Queries ◽  
Multiple Queries ◽  
First Order ◽  
Junction Tree ◽  
Variable Elimination ◽  
Cluster Representation

A standard approach for inference in probabilistic formalisms with first-order constructs is lifted variable elimination (LVE) for single queries. To handle multiple queries efficiently, the lifted junction tree algorithm (LJT) employs a first-order cluster representation of a model and LVE as a subroutine. Both algorithms answer conjunctive queries of propositional random variables, shattering the model on the query, which causes unnecessary groundings for conjunctive queries of interchangeable variables. This paper presents parameterised queries as a means to avoid groundings, applying the lifting idea to queries. Parameterised queries enable LVE and LJT to compute answers faster, while compactly representing queries and answers.

scholarly journals A Data Complexity and Rewritability Tetrachotomy of Ontology-Mediated Queries with a Covering Axiom

2020 ◽  
Author(s):  
Olga Gerasimova ◽  
Stanislav Kikot ◽  
Agi Kurucz ◽  
Vladimir Podolskii ◽  
Michael Zakharyaschev
Keyword(s):  
Sufficient Conditions ◽  
Data Complexity ◽  
Conjunctive Queries ◽  
First Order ◽  
Path Queries

Aiming to understand the data complexity of answering conjunctive queries mediated by an axiom stating that a class is covered by the union of two other classes, we show that deciding their first-order rewritability is PSPACE-hard and obtain a number of sufficient conditions for membership in AC0, L, NL, and P. Our main result is a complete syntactic AC0/NL/P/CONP tetrachotomy of path queries under the assumption that the covering classes are disjoint.

scholarly journals On Querying Incomplete Information in Databases under Bag Semantics

2017 ◽  
Author(s):  
Marco Console ◽  
Paolo Guagliardo ◽  
Leonid Libkin
Keyword(s):  
Incomplete Data ◽  
Real Life ◽  
Relational Algebra ◽  
Approximation Schemes ◽  
Query Rewriting ◽  
Possible World ◽  
First Order ◽  
Minimum Number ◽  
Database Technology ◽  
Certain Answers

Querying incomplete data is an important task both in data management, and in many AI applications that use query rewriting to take advantage of relational database technology. Usually one looks for answers that are certain, i.e., true in every possible world represented by an incomplete database. For positive queries, expressed either in positive relational algebra or as unions of conjunctive queries, finding such answers can be done efficiently when databases and query answers are sets. Real-life databases however use bag, rather than set, semantics. For bags, instead of saying that a tuple is certainly in the answer, we have more detailed information: namely, the range of the numbers of occurrences of the tuple in query answers. We show that the behavior of positive queries is different under bag semantics: finding the minimum number of occurrences can still be done efficiently, but for maximum it becomes intractable. We use these results to investigate approximation schemes for computing certain answers to arbitrary first-order queries that have been proposed for set semantics. One of them cannot be adapted to bags, as it relies on the intractable maxima of occurrences, but another scheme only deals with minima, and we show how to adapt it to bag semantics without losing efficiency.

scholarly journals Towards Universal Languages for Tractable Ontology Mediated Query Answering

2020 ◽  
Vol 34 (03) ◽  
pp. 3049-3056
Author(s):  
Heng Zhang ◽  
Yan Zhang ◽  
Jia-Huai You ◽  
Zhiyong Feng ◽  
Guifei Jiang
Keyword(s):  
Query Languages ◽  
Query Answering ◽  
Data Complexity ◽  
Conjunctive Queries ◽  
Negative Side ◽  
First Order ◽  
Positive Side ◽  
Universal Language ◽  
Ontology Language ◽  
The Family

An ontology language for ontology mediated query answering (OMQA-language) is universal for a family of OMQA-languages if it is the most expressive one among this family. In this paper, we focus on three families of tractable OMQA-languages, including first-order rewritable languages and languages whose data complexity of the query answering is in AC0 or PTIME. On the negative side, we prove that there is, in general, no universal language for each of these families of languages. On the positive side, we propose a novel property, the locality, to approximate the first-order rewritability, and show that there exists a language of disjunctive embedded dependencies that is universal for the family of OMQA-languages with locality. All of these results apply to OMQA with query languages such as conjunctive queries, unions of conjunctive queries and acyclic conjunctive queries.

scholarly journals SOME MODEL THEORY OF GUARDED NEGATION

2018 ◽  
Vol 83 (04) ◽  
pp. 1307-1344
Author(s):  
VINCE BÁRÁNY ◽  
MICHAEL BENEDIKT ◽  
BALDER TEN CATE
Keyword(s):  
Modal Logic ◽  
Model Theory ◽  
Description Logics ◽  
Expressive Power ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Beth Definability ◽  
Order Translations ◽  
Certain Answers

AbstractThe Guarded Negation Fragment (GNFO) is a fragment of first-order logic that contains all positive existential formulas, can express the first-order translations of basic modal logic and of many description logics, along with many sentences that arise in databases. It has been shown that the syntax of GNFO is restrictive enough so that computational problems such as validity and satisfiability are still decidable. This suggests that, in spite of its expressive power, GNFO formulas are amenable to novel optimizations. In this article we study the model theory of GNFO formulas. Our results include effective preservation theorems for GNFO, effective Craig Interpolation and Beth Definability results, and the ability to express the certain answers of queries with respect to a large class of GNFO sentences within very restricted logics.

scholarly journals Query Answering for Existential Rules via Efficient Datalog Rewriting

2020 ◽  
Author(s):  
Zhe Wang ◽  
Peng Xiao ◽  
Kewen Wang ◽  
Zhiqiang Zhuang ◽  
Hai Wan
Keyword(s):  
State Of The Art ◽  
Query Answering ◽  
Prototype System ◽  
High Complexity ◽  
Conjunctive Queries ◽  
First Order ◽  
Wide Range ◽  
Comparable Performance

Existential rules are an expressive ontology formalism for ontology-mediated query answering and thus query answering is of high complexity, while several tractable fragments have been identified. Existing systems based on first-order rewriting methods can lead to queries too large for DBMS to handle. It is shown that datalog rewriting can result in more compact queries, yet previously proposed datalog rewriting methods are mostly inefficient for implementation. In this paper, we fill the gap by proposing an efficient datalog rewriting approach for answering conjunctive queries over existential rules, and identify and combine existing fragments of existential rules for which our rewriting method terminates. We implemented a prototype system Drewer, and experiments show that it is able to handle a wide range of benchmarks in the literature. Moreover, Drewer shows superior or comparable performance over state-of-the-art systems on both the compactness of rewriting and the efficiency of query answering.

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