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 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 Programming Language for the Inductive Sets, and Applications

1982 ◽  
Vol 11 (143) ◽  
Author(s):  
David Harel ◽  
Dexter Kozen
Keyword(s):  
Programming Language ◽  
Relational Database ◽  
Query Language ◽  
Dynamic Logic ◽  
Computational Approach ◽  
Turing Machines ◽  
First Order ◽  
Separation Result ◽  
Alternating Turing Machines ◽  
Order Structures

We introduce a programming language IND that generalizes alternating Turing machines to arbitrary first-order structures. We show that IND programs (respectively, everywhere-halting IND programs, loop-free IND programs) accept precisely the inductively definable (respectively, hyperelementary, elementary) relations. We give several examples showing how the language provides a robust and computational approach to the theory of first-order inductive definability. We then show: (1) on all acceptable structures (in the sense of Moschovakis), r.e. Dynamic Logic is more expressive than finite-test Dynamic Logic. This refines a separation result of Meyer and Parikh; (2) IND provides a natural query language for the set of fixpoint queries over a relational database, answering a question of Chandra and Harel.

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 Temporal Query Answering in DL-Lite with Negation

10.29007/2df8 ◽  
2018 ◽  
Author(s):  
Stefan Borgwardt ◽  
Veronika Thost
Keyword(s):  
Temporal Logic ◽  
Domain Knowledge ◽  
Relational Databases ◽  
Query Language ◽  
Description Logics ◽  
Query Answering ◽  
Open World ◽  
Temporal Query ◽  
Temporal Query Language ◽  
Open World Assumption

Ontology-based query answering augments classical query answering in databases by adopting the open-world assumption and by including domain knowledge provided by an ontology. We investigate temporal query answering w.r.t. ontologies formulated in DL-Lite, a family of description logics that captures the conceptual features of relational databases and was tailored for efficient query answering. We consider a recently proposed temporal query language that combines conjunctive queries with the operators of propositional linear temporal logic (LTL). In particular, we consider negation in the ontology and query language, and study both data and combined complexity of query entailment.

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 Ontology-Based Query Answering for Probabilistic Temporal Data

2019 ◽  
Vol 33 ◽  
pp. 2903-2910 ◽  
Author(s):  
Patrick Koopmann
Keyword(s):  
Query Language ◽  
Linear Time ◽  
Uncertain Data ◽  
Query Answering ◽  
Temporal Data ◽  
Situation Recognition ◽  
Stream Reasoning ◽  
Time Logic ◽  
Probability Operators ◽  
The Cost

We investigate ontology-based query answering for data that are both temporal and probabilistic, which might occur in contexts such as stream reasoning or situation recognition with uncertain data. We present a framework that allows to represent temporal probabilistic data, and introduce a query language with which complex temporal and probabilistic patterns can be described. Specifically, this language combines conjunctive queries with operators from linear time logic as well as probability operators. We analyse the complexities of evaluating queries in this language in various settings. While in some cases, combining the temporal and the probabilistic dimension in such a way comes at the cost of increased complexity, we also determine cases for which this increase can be avoided.

Cooperative Query Processing via Knowledge Abstraction and Query Relaxation

2002 ◽  
pp. 211-228 ◽  
Author(s):  
Soon-Young Huh ◽  
Kae-Hyun Moon ◽  
Jin-Kyun Ahn
Keyword(s):  
Query Language ◽  
Database Systems ◽  
Query Answering ◽  
Prototype System ◽  
Levels Of Abstraction ◽  
Semantic Data ◽  
Approximate Query Answering ◽  
Approximate Query ◽  
Approximate Answers ◽  
General Fact

As database users adopt a query language to obtain information from a database, a more intelligent query answering system is increasingly needed that cooperates with the users to provide informative responses by understanding the intent behind a query. The effectiveness of decision support would improve significantly if the query answering system returned approximate answers rather than a null information response when there is no matching data available. Even when exact answers are found, neighboring information is still useful to users if the query is intended to explore some hypothetical information or abstract general fact. This chapter proposes an abstraction hierarchy as a framework to practically derive such approximate answers from ordinary everyday databases. It provides a knowledge abstraction database to facilitate the approximate query answering. The knowledge abstraction database specifically adopts an abstraction approach to extract semantic data relationships from the underlying database, and uses a multi-level hierarchy for coupling multiple levels of abstraction knowledge and data values. In cooperation with the underlying database, the knowledge abstraction database allows the relaxation of query conditions so that the original query scope can be broadened and thus information approximate to exact answers can be obtained. Conceptually abstract queries can also be posed to provide a less rigid query interface. A prototype system has been implemented at KAIST and is being tested with a personnel database system to demonstrate the usefulness and practicality of the knowledge abstraction database in ordinary database systems.

Deploying spatial-stream query answering in C-ITS scenarios1

Semantic Web ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 41-77
Author(s):  
Thomas Eiter ◽  
Ryutaro Ichise ◽  
Josiane Xavier Parreira ◽  
Patrik Schneider ◽  
Lihua Zhao
Keyword(s):  
Autonomous Vehicles ◽  
Query Language ◽  
Spatial Relations ◽  
Domain Model ◽  
Query Answering ◽  
Use Cases ◽  
Transport Systems ◽  
Local Dynamic ◽  
Spatio Temporal ◽  
Events Detection

Cooperative Intelligent Transport Systems (C-ITS) play an important role for providing the means to collect and exchange spatio-temporal data via V2X-based communication between vehicles and the infrastructure, which will become a central enabler for road safety of (semi)-autonomous vehicles. The Local Dynamic Map (LDM) is a key concept for integrating static and streamed data in a spatial context. The LDM has been semantically enhanced to allow for an elaborate domain model that is captured by a mobility ontology, and for queries over data streams that cater for semantic concepts and spatial relationships. Our approach for semantic enhancement is in the context of ontology-mediated query answering (OQA) and features conjunctive queries over DL-LiteA ontologies that support window operators over streams and spatial relations between spatial objects. In this paper, we show how this approach can be extended to address a wider range of use cases in the three C-ITS scenarios traffic statistics, traffic events detection, and advanced driving assistance systems. We define for the mentioned use cases requirements derived from necessary domain-specific features and report, based on them, on extensions of our query language and ontology model. The extensions include temporal relations, numeric predictions and trajectory predictions as well as optimization strategies such as caching. An experimental evaluation of queries that reflect the requirements has been conducted using the real-world traffic simulation tool PTV Vissim. It provides evidence for the feasibility/efficiency of our approach in the new scenarios.

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.

Application of Modified Bloch Waves to Image Analysis of Extended Linear Defects

1974 ◽  
Vol 32 ◽  
pp. 402-403
Author(s):  
S. Nakahara ◽  
D. M. Maher
Keyword(s):  
Image Analysis ◽  
Computational Approach ◽  
Dislocation Loops ◽  
Plane Wave Expansion ◽  
Dynamical Equations ◽  
Bloch Waves ◽  
Linear Defects ◽  
Imperfect Crystal ◽  
Localized Defects ◽  
Defective Crystals

Since Head first demonstrated the advantages of computer displayed theoretical intensities from defective crystals, computer display techniques have become important in image analysis. However the computational methods employed resort largely to numerical integration of the dynamical equations of electron diffraction. As a consequence, the interpretation of the results in terms of the defect displacement field and diffracting variables is difficult to follow in detail. In contrast to this type of computational approach which is based on a plane-wave expansion of the excited waves within the crystal (i.e. Darwin representation ), Wilkens assumed scattering of modified Bloch waves by an imperfect crystal. For localized defects, the wave amplitudes can be described analytically and this formulation has been used successfully to predict the black-white symmetry of images arising from small dislocation loops.

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