scholarly journals Learning Description Logic Concepts: When can Positive and Negative Examples be Separated?

2019 ◽  
Author(s):  
Maurice Funk ◽  
Jean Christoph Jung ◽  
Carsten Lutz ◽  
Hadrien Pulcini ◽  
Frank Wolter
Keyword(s):  
Decision Problem ◽  
Description Logic ◽  
Fundamental Question ◽  
Polynomial Hierarchy ◽  
Data Complexity ◽  
Conjunctive Queries ◽  
Complexity Results ◽  
Significant Attention

Learning description logic (DL) concepts from positive and negative examples given in the form of labeled data items in a KB has received significant attention in the literature. We study the fundamental question of when a separating DL concept exists and provide useful model-theoretic characterizations as well as complexity results for the associated decision problem. For expressive DLs such as ALC and ALCQI, our characterizations show a surprising link to the evaluation of ontology-mediated conjunctive queries. We exploit this to determine the combined complexity (between ExpTime and NExpTime) and data complexity (second level of the polynomial hierarchy) of separability. For the Horn DL EL, separability is ExpTime-complete both in combined and in data complexity while for its modest extension ELI it is even undecidable. Separability is also undecidable when the KB is formulated in ALC and the separating concept is required to be in EL or ELI.

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 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 Ontology-Mediated Querying with the Description Logic EL: Trichotomy and Linear Datalog Rewritability

2017 ◽  
Author(s):  
Carsten Lutz ◽  
Leif Sabellek
Keyword(s):  
Description Logic ◽  
Order Logic ◽  
First Order Logic ◽  
Data Complexity ◽  
First Order ◽  
Fine Grained ◽  
Linear Recursion

We consider ontology-mediated queries (OMQs) based on an EL ontology and an atomic query (AQ), provide an ultimately fine-grained analysis of data complexity and study rewritability into linear Datalog-aiming to capture linear recursion in SQL. Our main results are that every such OMQ is in AC0, NL-complete or PTime-complete, and that containment in NL coincides with rewritability into linear Datalog (whereas containment in AC0 coincides with rewritability into first-order logic). We establish natural characterizations of the three cases, show that deciding linear Datalog rewritability (as well as the mentioned complexities) is ExpTime-complete, give a way to construct linear Datalog rewritings when they exist, and prove that there is no constant bound on the arity of IDB relations in linear Datalog rewritings.

Fuzzy MCDM Approach for Make or Buy Decision Problem

2014 ◽  
pp. 978-995 ◽  
Author(s):  
Ferhan Çebi ◽  
İrem Otay ◽  
Dilay Çelebi
Keyword(s):  
Decision Problem ◽  
Real Life ◽  
Fundamental Question ◽  
Multi Criteria Decision Making ◽  
Manufacturing Strategy ◽  
Weighting Method ◽  
Second Stage ◽  
Solution Methods ◽  
Simple Additive Weighting ◽  
A Company

Make or buy decision answers a fundamental question in the development of a manufacturing strategy. It requires consideration of both quantitative and qualitative factors diverging in a broad range. This study presents a two-stage decision model which incorporates fuzzy multi-criteria decision making methods to support make or buy decision of a company operating in the wood building products sector. The first stage comprises fuzzy SAW (Simple Additive Weighting) method to evaluate the decision on market entry, then the second stage integrates fuzzy SAW and fuzzy VIKOR (Multi-criteria optimization and compromise solution) methods to evaluate sourcing options. Proposed approach is demonstrated on an example invoked from a real-life problem. Then, sensitivity analysis is conducted to test the robustness of the models.

scholarly journals Exploiting conjunctive queries in description logic programs

2008 ◽  
Vol 53 (1-4) ◽  
pp. 115-152 ◽  
Author(s):  
Thomas Eiter ◽  
Giovambattista Ianni ◽  
Thomas Krennwallner ◽  
Roman Schindlauer
Keyword(s):  
Description Logic ◽  
Logic Programs ◽  
Conjunctive Queries

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 The Logical Difference for the Lightweight Description Logic EL

2012 ◽  
Vol 44 ◽  
pp. 633-708 ◽  
Author(s):  
B. Konev ◽  
M. Ludwig ◽  
D. Walther ◽  
F. Wolter
Keyword(s):  
Polynomial Time ◽  
Description Logic ◽  
Snomed Ct ◽  
Conjunctive Queries ◽  
Polynomial Time Algorithms ◽  
The Difference

We study a logic-based approach to versioning of ontologies. Under this view, ontologies provide answers to queries about some vocabulary of interest. The difference between two versions of an ontology is given by the set of queries that receive different answers. We investigate this approach for terminologies given in the description logic EL extended with role inclusions and domain and range restrictions for three distinct types of queries: subsumption, instance, and conjunctive queries. In all three cases, we present polynomial-time algorithms that decide whether two terminologies give the same answers to queries over a given vocabulary and compute a succinct representation of the difference if it is non- empty. We present an implementation, CEX2, of the developed algorithms for subsumption and instance queries and apply it to distinct versions of Snomed CT and the NCI ontology.

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.

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