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 Temporal Minimal-World Query Answering over Sparse ABoxes

2021 ◽  
pp. 1-36
Author(s):  
STEFAN BORGWARDT ◽  
WALTER FORKEL ◽  
ALISA KOVTUNOVA
Keyword(s):  
Real World ◽  
Description Logic ◽  
Medical Data ◽  
Query Answering ◽  
Closed Domain ◽  
Data Complexity ◽  
Temporal Dimension ◽  
Health Records ◽  
Closed World ◽  
Real World Applications

Abstract 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. Many real-world applications, like processing electronic health records, also contain a temporal dimension and require efficient reasoning algorithms. Moreover, since medical data are not recorded on a regular basis, reasoners must deal with sparse data with potentially large temporal gaps. Our contribution consists of two main parts: In the first part, we introduce a new closed-world semantics for answering conjunctive queries (CQs) with negation over ontologies formulated in the description logic $${\mathcal E}{\mathcal L}{{\mathcal H}_ \bot }$$ , which is 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. In the second part, we extend this minimal-world semantics for answering metric temporal CQs with negation over the lightweight temporal logic and obtain similar rewritability and complexity results.

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.

Reasoning on the Semantic Web

2011 ◽  
pp. 110-133
Author(s):  
R. Brussee
Keyword(s):  
Real World ◽  
Description Logic ◽  
World Knowledge ◽  
Closed World Assumption ◽  
Sharp Distinction ◽  
Ontology Language ◽  
Closed World ◽  
Present Information ◽  
Logical Modeling ◽  
Case Reasoning

We describe reasoning as the process needed for using logic. Efficiently performing this process is a prerequisite for using logic to present information in a declarative way and to construct models of reality. In particular we describe description logic and the owl ontology language and explain that in this case reasoning amounts to graph completion operations that can be performed by a computer program. We give an extended example, modeling a building with wireless routers and explain how such a model can help in determining the location of resources. We emphasize how different assumptions on the way routers and buildings work are formalized and made explicit in our logical modeling, and explain the sharp distinction between knowing some facts and knowing all facts (open vs. closed world assumption). This should be helpful when using ontologies in applications needing incomplete real world knowledge.

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 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 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 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.

scholarly journals Actively Learning Concepts and Conjunctive Queries under ELr-Ontologies

2021 ◽  
Author(s):  
Maurice Funk ◽  
Jean Christoph Jung ◽  
Carsten Lutz
Keyword(s):  
Active Learning ◽  
Polynomial Time ◽  
Description Logic ◽  
Learning Algorithm ◽  
Domain Expert ◽  
Conjunctive Queries ◽  
Membership Queries ◽  
Equivalence Queries

We consider the problem to learn a concept or a query in the presence of an ontology formulated in the description logic ELr, in Angluin's framework of active learning that allows the learning algorithm to interactively query an oracle (such as a domain expert). We show that the following can be learned in polynomial time: (1) EL-concepts, (2) symmetry-free ELI-concepts, and (3) conjunctive queries (CQs) that are chordal, symmetry-free, and of bounded arity. In all cases, the learner can pose to the oracle membership queries based on ABoxes and equivalence queries that ask whether a given concept/query from the considered class is equivalent to the target. The restriction to bounded arity in (3) can be removed when we admit unrestricted CQs in equivalence queries. We also show that EL-concepts are not polynomial query learnable in the presence of ELI-ontologies.

Datalog Rewritability and Data Complexity of ALCHOIF with Closed Predicates

2020 ◽  
Author(s):  
Tomasz Gogacz ◽  
Sanja Lukumbuzya ◽  
Magdalena Ortiz ◽  
Mantas Šimkus
Keyword(s):  
Description Logic ◽  
Answer Set Programming ◽  
Query Answering ◽  
Stable Model ◽  
Data Complexity ◽  
First Order ◽  
Time Translation ◽  
Np Complete ◽  
Ontology Languages

We study the relative expressiveness of ontology-mediated queries (OMQs) formulated in the expressive Description Logic ALCHOIF extended with closed predicates. In particular, we present a polynomial-time translation from OMQs into Datalog with negation under the stable model semantics, the formalism that underlies Answer Set Programming. This is a novel and non-trivial result: the considered OMQs are not only non-monotonic but also feature a tricky combination of nominals, inverse roles, and role functionality. We start with atomic queries and then lift our approach to a large class of first-order queries where quantification is “guarded” by closed predicates. Our translation is based on a characterization of the query answering problem via integer programming, and a specially crafted program in Datalog with negation that finds solutions to dynamically generated systems of integer inequalities. As an important by-product of our translation, we get that the query answering problem is co-NP-complete in data complexity for the considered class of OMQs. Thus, answering these OMQs in the presence of closed predicates is not harder than answering them in the standard setting. This is not obvious as closed predicates are known to increase data complexity for some existing ontology languages.

scholarly journals Towards Universal Languages for Tractable Ontology Mediated Query Answering

2020 ◽  
Vol 34 (03) ◽  
pp. 3049-3056
Author(s):  
Heng Zhang ◽  
Yan Zhang ◽  
Jia-Huai You ◽  
Zhiyong Feng ◽  
Guifei Jiang
Keyword(s):  
Query Languages ◽  
Query Answering ◽  
Data Complexity ◽  
Conjunctive Queries ◽  
Negative Side ◽  
First Order ◽  
Positive Side ◽  
Universal Language ◽  
Ontology Language ◽  
The Family

An ontology language for ontology mediated query answering (OMQA-language) is universal for a family of OMQA-languages if it is the most expressive one among this family. In this paper, we focus on three families of tractable OMQA-languages, including first-order rewritable languages and languages whose data complexity of the query answering is in AC0 or PTIME. On the negative side, we prove that there is, in general, no universal language for each of these families of languages. On the positive side, we propose a novel property, the locality, to approximate the first-order rewritability, and show that there exists a language of disjunctive embedded dependencies that is universal for the family of OMQA-languages with locality. All of these results apply to OMQA with query languages such as conjunctive queries, unions of conjunctive queries and acyclic conjunctive queries.

Sign in / Sign up

Export Citation Format

Share Document