scholarly journals Reasoning about Explanations for Negative Query Answers in DL-Lite

2013 ◽  
Vol 48 ◽  
pp. 635-669 ◽  
Author(s):  
D. Calvanese ◽  
M. Ortiz ◽  
M. Simkus ◽  
G. Stefanoni
Keyword(s):  
Computational Complexity ◽  
Description Logics ◽  
Query Answering ◽  
Abductive Reasoning ◽  
Arbitrary Subset ◽  
Conjunctive Query ◽  
Query Answer ◽  
Reasoning Tasks ◽  
Usability Requirements

In order to meet usability requirements, most logic-based applications provide explanation facilities for reasoning services. This holds also for Description Logics, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tuple in a query answer, it is important to explain also why a given tuple is missing. We address the latter problem for instance and conjunctive query answering over DL-Lite ontologies by adopting abductive reasoning; that is, we look for additions to the ABox that force a given tuple to be in the result. As reasoning tasks we consider existence and recognition of an explanation, and relevance and necessity of a given assertion for an explanation. We characterize the computational complexity of these problems for arbitrary, subset minimal, and cardinality minimal explanations.

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 Ontology-Mediated Querying with Horn Description Logics

2020 ◽  
Vol 34 (4) ◽  
pp. 533-537 ◽  
Author(s):  
Leif Sabellek
Keyword(s):  
Computational Complexity ◽  
Description Logics ◽  
Data Access ◽  
Logical Reasoning ◽  
Data Complexity ◽  
Conjunctive Query ◽  
Database Query ◽  
Query By Example ◽  
Open Questions ◽  
Verification Problem

AbstractAn ontology-mediated query (OMQ) consists of a database query paired with an ontology. When evaluated on a database, an OMQ returns not only the answers that are already in the database, but also those answers that can be obtained via logical reasoning using rules from ontology. There are many open questions regarding the complexities of problems related to OMQs. Motivated by the use of ontologies in practice, new reasoning problems which have never been considered in the context of ontologies become relevant, since they can improve the usability of ontology enriched systems. This thesis deals with various reasoning problems that emerge from ontology-mediated querying and it investigates the computational complexity of these problems. We focus on ontologies formulated in Horn description logics, which are a popular choice for ontologies in practice. In particular, the thesis gives results regarding the data complexity of OMQ evaluation by completely classifying complexity and rewritability questions for OMQs based on an EL ontology and a conjunctive query. Furthermore, the query-by-example problem, and the expressibility and verification problem in ontology-based data access are introduced and investigated.

scholarly journals Complexity of Inconsistency-Tolerant Query Answering in Datalog+/– under Cardinality-Based Repairs

2019 ◽  
Vol 33 ◽  
pp. 2962-2969 ◽  
Author(s):  
Thomas Lukasiewicz ◽  
Enrico Malizia ◽  
Andrius Vaicenavičius
Keyword(s):  
Computational Complexity ◽  
Knowledge Bases ◽  
Query Answering ◽  
Conjunctive Query ◽  
Wide Range ◽  
Consistent Subset

Querying inconsistent ontological knowledge bases is an important problem in practice, for which several inconsistencytolerant query answering semantics have been proposed, including query answering relative to all repairs, relative to the intersection of repairs, and relative to the intersection of closed repairs. In these semantics, one assumes that the input database is erroneous, and the notion of repair describes a maximally consistent subset of the input database, where different notions of maximality (such as subset and cardinality maximality) are considered. In this paper, we give a precise picture of the computational complexity of inconsistencytolerant (Boolean conjunctive) query answering in a wide range of Datalog± languages under the cardinality-based versions of the above three repair semantics.

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.

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).

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