scholarly journals Cardinality Queries over DL-Lite Ontologies

2021 ◽  
Author(s):  
Meghyn Bienvenu ◽  
Quentin Manière ◽  
Michaël Thomazo
Keyword(s):  
Automated Reasoning ◽  
Query Language ◽  
Heterogeneous Data ◽  
Query Answering ◽  
Canonical Model ◽  
Data Complexity ◽  
Complex Behaviour ◽  
New Approach ◽  
Recent Interest ◽  
Structured Knowledge

Ontology-mediated query answering (OMQA) employs structured knowledge and automated reasoning in order to facilitate access to incomplete and possibly heterogeneous data. While most research on OMQA adopts (unions of) conjunctive queries as the query language, there has been recent interest in handling queries that involve counting. In this paper, we advance this line of research by investigating cardinality queries (which correspond to Boolean atomic counting queries) coupled with DL-Lite ontologies. Despite its apparent simplicity, we show that such an OMQA setting gives rise to rich and complex behaviour. While we prove that cardinality query answering is tractable (TC0) in data complexity when the ontology is formulated in DL-Lite-core, the problem becomes coNP-hard as soon as role inclusions are allowed. For DL-Lite-pos-H (which allows only positive axioms), we establish a P-coNP dichotomy and pinpoint the TC0 cases; for DL-Lite-core-H (allowing also negative axioms), we identify new sources of coNP complexity and also exhibit L-complete cases. Interestingly, and in contrast to related tractability results, we observe that the canonical model may not give the optimal count value in the tractable cases, which led us to develop an entirely new approach based upon exploring a space of strategies to determine the minimum possible number of query matches.

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.

scholarly journals Closed-World Semantics for Conjunctive Queries with Negation over ELH-bottom Ontologies

2019 ◽  
Author(s):  
Stefan Borgwardt ◽  
Walter Forkel
Keyword(s):  
Polynomial Time ◽  
Description Logic ◽  
Background Knowledge ◽  
Query Answering ◽  
Canonical Model ◽  
Closed Domain ◽  
Data Complexity ◽  
Conjunctive Queries ◽  
Closed World Assumption ◽  
Closed World

Ontology-mediated query answering is a popular paradigm for enriching answers to user queries with background knowledge.  For querying the absence of information, however, there exist only few ontology-based approaches.  Moreover, these proposals conflate the closed-domain and closed-world assumption, and therefore are not suited to deal with the anonymous objects that are common in ontological reasoning. We propose a new closed-world semantics for answering conjunctive queries with negation over ontologies formulated in the description logic ELH-bottom, based on the minimal canonical model.  We propose a rewriting strategy for dealing with negated query atoms, which shows that query answering is possible in polynomial time in data complexity.

scholarly journals Filtering Search: A New Approach to Query-Answering

1986 ◽  
Vol 15 (3) ◽  
pp. 703-724 ◽  
Author(s):  
Bernard Chazelle
Keyword(s):  
Query Answering ◽  
New Approach

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 A New Approach to Detection of Changes in Multidimensional Patterns

2020 ◽  
Vol 10 (2) ◽  
pp. 125-136 ◽  
Author(s):  
Tomasz Gałkowski ◽  
Adam Krzyżak ◽  
Zbigniew Filutowicz
Keyword(s):  
Kernel Estimation ◽  
Detection Algorithm ◽  
Heterogeneous Data ◽  
Data Types ◽  
New Approach ◽  
Abrupt Changes ◽  
Changes Detection ◽  
Data Collections ◽  
Derivatives Of

AbstractNowadays, unprecedented amounts of heterogeneous data collections are stored, processed and transmitted via the Internet. In data analysis one of the most important problems is to verify whether data observed or/and collected in time are genuine and stationary, i.e. the information sources did not change their characteristics. There is a variety of data types: texts, images, audio or video files or streams, metadata descriptions, thereby ordinary numbers. All of them changes in many ways. If the change happens the next question is what is the essence of this change and when and where the change has occurred. The main focus of this paper is detection of change and classification of its type. Many algorithms have been proposed to detect abnormalities and deviations in the data. In this paper we propose a new approach for abrupt changes detection based on the Parzen kernel estimation of the partial derivatives of the multivariate regression functions in presence of probabilistic noise. The proposed change detection algorithm is applied to oneand two-dimensional patterns to detect the abrupt changes.

scholarly journals Revisiting Controlled Query Evaluation in Description Logics

2019 ◽  
Author(s):  
Domenico Lembo ◽  
Riccardo Rosati ◽  
Domenico Fabio Savo
Keyword(s):  
Private Information ◽  
Description Logics ◽  
Study Data ◽  
Query Answering ◽  
Query Evaluation ◽  
Data Complexity ◽  
Complexity Results ◽  
Controlled Query Evaluation ◽  
Consistent Query Answering ◽  
The Relationship

Controlled Query Evaluation (CQE) is a confidentiality-preserving framework in which private information is protected through a policy, and a (optimal) censor guarantees that answers to queries are maximized without violating the policy. CQE has been recently studied in the context of ontologies, where the focus has been mainly on the problem of the existence of an optimal censor. In this paper we instead consider query answering over all possible optimal censors. We study data complexity of this problem for ontologies specified in the Description Logics DL-LiteR and EL_bottom and for variants of the censor language, which is the language used by the censor to enforce the policy. In our investigation we also analyze the relationship between CQE and the problem of Consistent Query Answering (CQA). Some of the complexity results we provide are indeed obtained through mutual reduction between CQE and CQA.

scholarly journals Controlled Query Evaluation in Description Logics Through Instance Indistinguishability

2020 ◽  
Author(s):  
Gianluca Cima ◽  
Domenico Lembo ◽  
Riccardo Rosati ◽  
Domenico Fabio Savo
Keyword(s):  
Description Logics ◽  
Privacy Preserving ◽  
Query Answering ◽  
Query Evaluation ◽  
Data Complexity ◽  
First Order ◽  
Complexity Results ◽  
Controlled Query Evaluation

We study privacy-preserving query answering in Description Logics (DLs). Specifically, we consider the approach of controlled query evaluation (CQE) based on the notion of instance indistinguishability. We derive data complexity results for query answering over DL-LiteR ontologies, through a comparison with an alternative, existing confidentiality-preserving approach to CQE. Finally, we identify a semantically well-founded notion of approximated query answering for CQE, and prove that, for DL-LiteR ontologies, this form of CQE is tractable with respect to data complexity and is first-order rewritable, i.e., it is always reducible to the evaluation of a first-order query over the data instance.

scholarly journals Capturing Homomorphism-Closed Decidable Queries with Existential Rules

2021 ◽  
Author(s):  
Camille Bourgaux ◽  
David Carral ◽  
Markus Krötzsch ◽  
Sebastian Rudolph ◽  
Michaël Thomazo
Keyword(s):  
Query Language ◽  
Computational Approach ◽  
Query Answering ◽  
Rule Set

Existential rules are a very popular ontology-mediated query language for which the chase represents a generic computational approach for query answering. It is straightforward that existential rule queries exhibiting chase termination are decidable and can only recognize properties that are preserved under homomorphisms. In this paper, we show the converse: every decidable query that is closed under homomorphism can be expressed by an existential rule set for which the standard chase universally terminates. Membership in this fragment is not decidable, but we show via a diagonalisation argument that this is unavoidable.

scholarly journals Teaching and Learning with Structured Knowledge Maps: An Analysis about the New Approach

2016 ◽  
Vol 07 (15) ◽  
pp. 2212-2225
Author(s):  
Nayara Silva Costa ◽  
Carlos Alberto Lopes da Silva ◽  
Daniela Carvalho Monteiro Ferreira ◽  
Luciano Vieira Lima
Keyword(s):  
Teaching And Learning ◽  
Knowledge Maps ◽  
New Approach ◽  
Structured Knowledge

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.

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