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 Nominals, Inverses, Counting, and Conjunctive Queries or: Why Infinity is your Friend!

2010 ◽  
Vol 39 ◽  
pp. 429-481 ◽  
Author(s):  
S. Rudolph ◽  
B. Glimm
Keyword(s):  
Knowledge Representation ◽  
Description Logic ◽  
Query Language ◽  
Description Logics ◽  
Knowledge Bases ◽  
Conjunctive Query ◽  
Conjunctive Queries ◽  
Decidability Result ◽  
Wide Range ◽  
Significant Attention

Description Logics are knowledge representation formalisms that provide, for example, the logical underpinning of the W3C OWL standards. Conjunctive queries, the standard query language in databases, have recently gained significant attention as an expressive formalism for querying Description Logic knowledge bases. Several different techniques for deciding conjunctive query entailment are available for a wide range of DLs. Nevertheless, the combination of nominals, inverse roles, and number restrictions in OWL 1 and OWL 2 DL causes unsolvable problems for the techniques hitherto available. We tackle this problem and present a decidability result for entailment of unions of conjunctive queries in the DL ALCHOIQb that contains all three problematic constructors simultaneously. Provided that queries contain only simple roles, our result also shows decidability of entailment of (unions of) conjunctive queries in the logic that underpins OWL 1 DL and we believe that the presented results will pave the way for further progress towards conjunctive query entailment decision procedures for the Description Logics underlying the OWL standards.

scholarly journals Regular Path Queries in Lightweight Description Logics: Complexity and Algorithms

2015 ◽  
Vol 53 ◽  
pp. 315-374 ◽  
Author(s):  
Meghyn Bienvenu ◽  
Magdalena Ortiz ◽  
Mantas Simkus
Keyword(s):  
Description Logic ◽  
Query Language ◽  
Description Logics ◽  
Knowledge Bases ◽  
Query Answering ◽  
Complexity Bounds ◽  
Regular Path ◽  
Regular Path Queries ◽  
Path Navigation ◽  
Path Queries

Conjunctive regular path queries are an expressive extension of the well-known class of conjunctive queries. Such queries have been extensively studied in the (graph) database community, since they support a controlled form of recursion and enable sophisticated path navigation. Somewhat surprisingly, there has been little work aimed at using such queries in the context of description logic (DL) knowledge bases, particularly for the lightweight DLs that are considered best suited for data-intensive applications. This paper aims to bridge this gap by providing algorithms and tight complexity bounds for answering two-way conjunctive regular path queries over DL knowledge bases formulated in lightweight DLs of the DL-Lite and EL families. Our results demonstrate that in data complexity, the cost of moving to this richer query language is as low as one could wish for: the problem is NL-complete for DL-Lite and P-complete for EL. The combined complexity of query answering increases from NP- to PSpace-complete, but for two-way regular path queries (without conjunction), we show that query answering is tractable even with respect to combined complexity. Our results reveal two-way conjunctive regular path queries as a promising language for querying data enriched by ontologies formulated in DLs of the DL-Lite and EL families or the corresponding OWL 2 QL and EL profiles.

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 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.

scholarly journals Answering Conjunctive Queries with Inequalities in DL-Liteℛ

2020 ◽  
Vol 34 (03) ◽  
pp. 2782-2789
Author(s):  
Gianluca Cima ◽  
Maurizio Lenzerini ◽  
Antonella Poggi
Keyword(s):  
Description Logic ◽  
Query Language ◽  
Query Answering ◽  
Data Complexity ◽  
Conjunctive Queries ◽  
Complexity Bounds ◽  
Ontology Language

In the context of the Description Logic DL-Liteℛ≠, i.e., DL-Liteℛ without UNA and with inequality axioms, we address the problem of adding to unions of conjunctive queries (UCQs) one of the simplest forms of negation, namely, inequality. It is well known that answering conjunctive queries with unrestricted inequalities over DL-Liteℛ ontologies is in general undecidable. Therefore, we explore two strategies for recovering decidability, and, hopefully, tractability. Firstly, we weaken the ontology language, and consider the variant of DL-Liteℛ≠ corresponding to rdfs enriched with both inequality and disjointness axioms. Secondly, we weaken the query language, by preventing inequalities to be applied to existentially quantified variables, thus obtaining the class of queries named UCQ≠,bs. We prove that in the two cases, query answering is decidable, and we provide tight complexity bounds for the problem, both for data and combined complexity. Notably, the results show that answering UCQ≠,bs over DL-Liteℛ≠ ontologies is still in AC0 in data complexity.

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 Taming the Infinite Chase: Query Answering under Expressive Relational Constraints

2013 ◽  
Vol 48 ◽  
pp. 115-174 ◽  
Author(s):  
A. Calì ◽  
G. Gottlob ◽  
M. Kifer
Keyword(s):  
Description Logics ◽  
Object Oriented ◽  
Query Answering ◽  
Conjunctive Query ◽  
Complexity Bounds ◽  
Ontology Language ◽  
Query Containment ◽  
Decidability And Complexity ◽  
Object Oriented Ontology ◽  
Syntactic Restrictions

The chase algorithm is a fundamental tool for query evaluation and for testing query containment under tuple-generating dependencies (TGDs) and equality-generating dependencies (EGDs). So far, most of the research on this topic has focused on cases where the chase procedure terminates. This paper introduces expressive classes of TGDs defined via syntactic restrictions: guarded TGDs (GTGDs) and weakly guarded sets of TGDs (WGTGDs). For these classes, the chase procedure is not guaranteed to terminate and thus may have an infinite outcome. Nevertheless, we prove that the problems of conjunctive-query answering and query containment under such TGDs are decidable. We provide decision procedures and tight complexity bounds for these problems. Then we show how EGDs can be incorporated into our results by providing conditions under which EGDs do not harmfully interact with TGDs and do not affect the decidability and complexity of query answering. We show applications of the aforesaid classes of constraints to the problem of answering conjunctive queries in F-Logic Lite, an object-oriented ontology language, and in some tractable Description Logics.

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 Answering Fuzzy Queries over Fuzzy DL-Lite Ontologies

2022 ◽  
pp. 1-30
Author(s):  
GABRIELLA PASI ◽  
RAFAEL PEÑALOZA
Keyword(s):  
Fuzzy Logic ◽  
Domain Knowledge ◽  
Description Logic ◽  
Classical Case ◽  
Point Of View ◽  
Query Answering ◽  
Data Complexity ◽  
Conjunctive Query ◽  
Triangular Norm ◽  
Mathematical Fuzzy Logic

Abstract A prominent problem in knowledge representation is how to answer queries taking into account also the implicit consequences of an ontology representing domain knowledge. While this problem has been widely studied within the realm of description logic ontologies, it has been surprisingly neglected within the context of vague or imprecise knowledge, particularly from the point of view of mathematical fuzzy logic. In this paper, we study the problem of answering conjunctive queries and threshold queries w.r.t. ontologies in fuzzy DL-Lite. Specifically, we show through a rewriting approach that threshold query answering w.r.t. consistent ontologies remains in ${AC}^{0}$ in data complexity, but that conjunctive query answering is highly dependent on the selected triangular norm, which has an impact on the underlying semantics. For the idempotent Gödel t-norm, we provide an effective method based on a reduction to the classical case.

Secrecy-Preserving Reasoning and Query Answering in Probabilistic Description Logic Knowledge Bases

10.29007/npd4 ◽  
2018 ◽  
Author(s):  
Gopalakrishnan Krishnasamy Sivaprakasam ◽  
Adrienne Raglin ◽  
Douglas Summers-Stay ◽  
Giora Slutzki
Keyword(s):  
Probabilistic Model ◽  
Description Logic ◽  
Knowledge Bases ◽  
Query Answering ◽  
Decomposition Algorithm ◽  
Probabilistic Description ◽  
Recursive Query ◽  
Finite Set ◽  
The Given

In this paper we study Secrecy-Preserving Query Answering problem underthe OpenWorld Assumption (OWA) for Prob-EL>0;=1 Knowledge Bases(KBs). We have designed a tableau procedure to compute a semi model Mover the given KB which eventually is equivalent to a probabilistic modelto KB. Given a secrecy set S, which is a finite set of assertions, wecompute a function E, called an envelope of S, which assigns a set E() ofassertions to each world in the semi modal M. E provides logical protection to the secrecy set S against the reasoning of a querying agent. Once the semi model M and an envelope E are computed, we define the secrecy-preserving semi model ME.Based on the information available in ME, assertional queries with probabilisticoperators can be answered eciently while preserving secrecy. Tothe best of our knowledge, this work is first one studying secrecy-preservingreasoning in description logic augmented with probabilistic operators. Whenthe querying agent asks a query q, the reasoner answers “Yes” if informationabout q is available in ME; otherwise, the reasoner answers “Unknown”. Beingable to answer “Unknown” plays a key role in protecting secrecy underOWA. Since we are not computing all the consequences of the knowledgebase, answers to the queries based on just secrecy-preserving semi modelME could be erroneous. To fix this problem, we further augment our algorithmsby providing recursive query decomposition algorithm to make thequery answering procedure foolproof.1

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