UCQ-Rewritings for disjunctive knowledge and queries with negated atoms

Semantic Web ◽  
2020 ◽  
pp. 1-25
Author(s):  
Enrique Matos Alfonso ◽  
Alexandros Chortaras ◽  
Giorgos Stamou
Keyword(s):  
Incomplete Data ◽  
Knowledge Bases ◽  
Query Answering ◽  
Query Rewriting ◽  
Conjunctive Queries

In this paper, we study the problem of query rewriting for disjunctive existential rules. Query rewriting is a well-known approach for query answering on knowledge bases with incomplete data. We propose a rewriting technique that uses negative constraints and conjunctive queries to remove the disjunctive components of disjunctive existential rules. This process eventually generates new non-disjunctive rules, i.e., existential rules. The generated rules can then be used to produce new rewritings using existing rewriting approaches for existential rules. With the proposed technique we are able to provide complete UCQ-rewritings for union of conjunctive queries with universally quantified negation. We implemented the proposed algorithm in the Completo system and performed experiments that evaluate the viability of the proposed solution.

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 Conjunctive Query Answering for the Description Logic SHIQ

2008 ◽  
Vol 31 ◽  
pp. 157-204 ◽  
Author(s):  
B. Glimm ◽  
C. Lutz ◽  
I. Horrocks ◽  
U. Sattler
Keyword(s):  
Description Logic ◽  
Query Language ◽  
Description Logics ◽  
Knowledge Bases ◽  
Deterministic Algorithm ◽  
Query Answering ◽  
Conjunctive Query ◽  
Conjunctive Queries ◽  
Complexity Bounds ◽  
Double Exponential

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, conjunctive query answering over DL knowledge bases is only poorly understood if transitive roles are admitted in the query. In this paper, we consider unions of conjunctive queries over knowledge bases formulated in the prominent DL SHIQ and allow transitive roles in both the query and the knowledge base. We show decidability of query answering in this setting and establish two tight complexity bounds: regarding combined complexity, we prove that there is a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query, which is optimal. Regarding data complexity, we prove containment in co-NP.

scholarly journals Answering Conjunctive Regular Path Queries over Guarded Existential Rules

2017 ◽  
Author(s):  
Jean-François Baget ◽  
Meghyn Bienvenu ◽  
Marie-Laure Mugnier ◽  
Michael Thomazo
Keyword(s):  
Knowledge Bases ◽  
Query Answering ◽  
Linear Case ◽  
Data Complexity ◽  
Conjunctive Queries ◽  
Regular Path ◽  
Regular Path Queries ◽  
Path Queries

Ontology-mediated query answering is concerned with the problem of answering queries over knowledge bases consisting of a database instance and an ontology. While most work in the area focuses on conjunctive queries, navigational queries are gaining increasing attention. In this paper, we investigate the complexity of answering two-way conjunctive regular path queries (CRPQs) over knowledge bases whose ontology is given by a set of guarded existential rules. We first consider the subclass of linear existential rules and show that CRPQ answering is EXPTIME-complete in combined complexity and NL-complete in data complexity, matching the recently established bounds for answering non-conjunctive RPQs. For guarded rules, we provide a non-trivial reduction to the linear case, which allows us to show that the complexity of CRPQ answering is the same as for plain conjunctive queries, namely, 2EXPTIME-complete in combined complexity and PTIME-complete in data complexity.

scholarly journals Reverse Engineering Queries in Ontology-Enriched Systems: The Case of Expressive Horn Description Logic Ontologies

2018 ◽  
Author(s):  
Víctor Gutiérrez-Basulto ◽  
Jean Christoph Jung ◽  
Leif Sabellek
Keyword(s):  
Reverse Engineering ◽  
Knowledge Base ◽  
Description Logic ◽  
Knowledge Bases ◽  
Query Answering ◽  
Conjunctive Queries ◽  
Complexity Bounds ◽  
Query By Example

We introduce the query-by-example (QBE) paradigm for query answering in the presence of ontologies. Intuitively, QBE permits non-expert users to explore the data by providing examples of the information they (do not) want, which the system then generalizes into a query. Formally, we study the following question: given a knowledge base and sets of positive and negative examples, is there a query that returns all positive but none of the negative examples?  We focus on description logic knowledge bases with ontologies formulated in Horn-ALCI and (unions of) conjunctive queries. Our main contributions are characterizations, algorithms and tight complexity bounds for QBE.  

scholarly journals Querying incomplete data over extended ER schemata

2010 ◽  
Vol 10 (3) ◽  
pp. 291-329 ◽  
Author(s):  
ANDREA CALÌ ◽  
DAVIDE MARTINENGHI
Keyword(s):  
Incomplete Data ◽  
Conceptual Modeling ◽  
Query Answering ◽  
Relational Data ◽  
Cardinality Constraints ◽  
Conjunctive Queries ◽  
Er Model ◽  
Entity Relationship ◽  
Data Design ◽  
Different Sources

AbstractSince Chen's Entity-Relationship (ER) model, conceptual modeling has been playing a fundamental role in relational data design. In this paper we consider an extended ER (EER) model enriched with cardinality constraints, disjointness assertions, and is a relations among both entities and relationships. In this setting, we consider the case of incomplete data, which is likely to occur, for instance, when data from different sources are integrated. In such a context, we address the problem of providing correct answers to conjunctive queries by reasoning on the schema. Based on previous results about decidability of the problem, we provide a query answering algorithm that performs rewriting of the initial query into a recursive Datalog query encoding the information about the schema. We finally show extensions to more general settings.

scholarly journals Query answering in circumscribed OWL2 profiles

2021 ◽  
Author(s):  
Piero A. Bonatti
Keyword(s):  
Description Logics ◽  
Knowledge Bases ◽  
Query Answering ◽  
Data Complexity ◽  
Conjunctive Query ◽  
Conjunctive Queries

AbstractThis paper partially bridges a gap in the literature on Circumscription in Description Logics by investigating the tractability of conjunctive query answering in OWL2’s profiles. It turns out that the data complexity of conjunctive query answering is coNP-hard in circumscribed $\mathcal {E}{\mathscr{L}}$ E L and DL-lite, while in circumscribed OWL2-RL conjunctive queries retain their classical semantics. In an attempt to capture nonclassical inferences in OWL2-RL, we consider conjunctive queries with safe negation. They can detect some of the nonclassical consequences of circumscribed knowledge bases, but data complexity becomes coNP-hard. In circumscribed $\mathcal {E}{\mathscr{L}}$ E L , answering queries with safe negation is undecidable.

An Improved Set-based Reasoner for the Description Logic 𝒟ℒD4,׆

2021 ◽  
Vol 178 (4) ◽  
pp. 315-346
Author(s):  
Domenico Cantone ◽  
Marianna Nicolosi-Asmundo ◽  
Daniele Francesco Santamaria
Keyword(s):  
Semantic Web ◽  
Set Theory ◽  
Description Logic ◽  
Knowledge Bases ◽  
Query Answering ◽  
Conjunctive Query ◽  
Classification Problems ◽  
Previous Version ◽  
Decidable Fragment ◽  
Stratified Set

We present a KE-tableau-based implementation of a reasoner for a decidable fragment of (stratified) set theory expressing the description logic 𝒟ℒ〈4LQSR,×〉(D) (𝒟ℒD4,×, for short). Our application solves the main TBox and ABox reasoning problems for 𝒟ℒD4,×. In particular, it solves the consistency and the classification problems for 𝒟ℒD4,×-knowledge bases represented in set-theoretic terms, and a generalization of the Conjunctive Query Answering problem in which conjunctive queries with variables of three sorts are admitted. The reasoner, which extends and improves a previous version, is implemented in C++. It supports 𝒟ℒD4,×-knowledge bases serialized in the OWL/XML format and it admits also rules expressed in SWRL (Semantic Web Rule Language).

scholarly journals Acyclicity Notions for Existential Rules and Their Application to Query Answering in Ontologies

2013 ◽  
Vol 47 ◽  
pp. 741-808 ◽  
Author(s):  
B. Cuenca Grau ◽  
I. Horrocks ◽  
M. Krötzsch ◽  
C. Kupke ◽  
D. Magka ◽  
...  
Keyword(s):  
Knowledge Representation ◽  
Sufficient Conditions ◽  
Query Answering ◽  
Conjunctive Queries ◽  
Practical Solution ◽  
Ontology Language ◽  
Lower Complexity ◽  
The Given ◽  
Theoretical Side

Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a prominent problem in knowledge representation and databases. This problem can be solved using the chase algorithm, which extends the given set of facts with fresh facts in order to satisfy the rules. If the chase terminates, then CQs can be evaluated directly in the resulting set of facts. The chase, however, does not terminate necessarily, and checking whether the chase terminates on a given set of rules and facts is undecidable. Numerous acyclicity notions were proposed as sufficient conditions for chase termination. In this paper, we present two new acyclicity notions called model-faithful acyclicity (MFA) and model-summarising acyclicity (MSA). Furthermore, we investigate the landscape of the known acyclicity notions and establish a complete taxonomy of all notions known to us. Finally, we show that MFA and MSA generalise most of these notions. Existential rules are closely related to the Horn fragments of the OWL 2 ontology language; furthermore, several prominent OWL 2 reasoners implement CQ answering by using the chase to materialise all relevant facts. In order to avoid termination problems, many of these systems handle only the OWL 2 RL profile of OWL 2; furthermore, some systems go beyond OWL 2 RL, but without any termination guarantees. In this paper we also investigate whether various acyclicity notions can provide a principled and practical solution to these problems. On the theoretical side, we show that query answering for acyclic ontologies is of lower complexity than for general ontologies. On the practical side, we show that many of the commonly used OWL 2 ontologies are MSA, and that the number of facts obtained by materialisation is not too large. Our results thus suggest that principled development of materialisation-based OWL 2 reasoners is practically feasible.

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