4,023 research outputs found
Module extraction via query inseparability in OWL 2 QL
We show that deciding conjunctive query inseparability for OWL 2 QL ontologies is PSpace-hard and in ExpTime. We give polynomial-time (incomplete) algorithms and demonstrate by experiments that they can be used for practical module extraction
Conjunctive query inseparability in OWL2QL is ExpTime-hard
We settle an open question on the complexity of the following problem: given two OWL2QL TBoxes and a signature, decide whether these TBoxes return the same answers to any conjunctive query over any data formulated in the given signature. It has been known that the complexity of this problem is between PSpace and ExpTime. Here we show that the problem is ExpTime-complete and, in fact, deciding whether two OWL2QL knowledge bases (each with its own data) give the same answers to any conjunctive query is ExpTime-hard
Conjunctive query inseparability of OWL 2 QL TBoxes
The OWL2 profile OWL 2 QL, based on the DL-Lite family of description logics, is emerging as a major language for developing new ontologies and approximating the existing ones. Its main application is ontology based data access, where ontologies are used to provide background knowledge for answering queries over data. We investigate the corresponding notion of query inseparability (or equivalence) for OWL 2 QL ontologies and show that deciding query inseparability is PSpace-hard and in ExpTime. We give polynomial-time (incomplete) algorithms and demonstrate by experiments that they can be used for practical module extraction
Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure
In this work we study a rational extension of the low complexity
description logic SROEL, which underlies the OWL EL ontology language. The
extension involves a typicality operator T, whose semantics is based on Lehmann
and Magidor's ranked models and allows for the definition of defeasible
inclusions. We consider both rational entailment and minimal entailment. We
show that deciding instance checking under minimal entailment is in general
-hard, while, under rational entailment, instance checking can be
computed in polynomial time. We develop a Datalog calculus for instance
checking under rational entailment and exploit it, with stratified negation,
for computing the rational closure of simple KBs in polynomial time.Comment: Accepted for publication on Fundamenta Informatica
Repairing Ontologies via Axiom Weakening.
Ontology engineering is a hard and error-prone task, in which
small changes may lead to errors, or even produce an inconsistent
ontology. As ontologies grow in size, the need for automated
methods for repairing inconsistencies while preserving
as much of the original knowledge as possible increases.
Most previous approaches to this task are based on removing
a few axioms from the ontology to regain consistency.
We propose a new method based on weakening these axioms
to make them less restrictive, employing the use of refinement
operators. We introduce the theoretical framework for
weakening DL ontologies, propose algorithms to repair ontologies
based on the framework, and provide an analysis of
the computational complexity. Through an empirical analysis
made over real-life ontologies, we show that our approach
preserves significantly more of the original knowledge of the
ontology than removing axioms
Constructing and Extending Description Logic Ontologies using Methods of Formal Concept Analysis
Description Logic (abbrv. DL) belongs to the field of knowledge representation and reasoning. DL researchers have developed a large family of logic-based languages, so-called description logics (abbrv. DLs). These logics allow their users to explicitly represent knowledge as ontologies, which are finite sets of (human- and machine-readable) axioms, and provide them with automated inference services to derive implicit knowledge. The landscape of decidability and computational complexity of common reasoning tasks for various description logics has been explored in large parts: there is always a trade-off between expressibility and reasoning costs. It is therefore not surprising that DLs are nowadays applied in a large variety of domains: agriculture, astronomy, biology, defense, education, energy management, geography, geoscience, medicine, oceanography, and oil and gas. Furthermore, the most notable success of DLs is that these constitute the logical underpinning of the Web Ontology Language (abbrv. OWL) in the Semantic Web.
Formal Concept Analysis (abbrv. FCA) is a subfield of lattice theory that allows to analyze data-sets that can be represented as formal contexts. Put simply, such a formal context binds a set of objects to a set of attributes by specifying which objects have which attributes. There are two major techniques that can be applied in various ways for purposes of conceptual clustering, data mining, machine learning, knowledge management, knowledge visualization, etc. On the one hand, it is possible to describe the hierarchical structure of such a data-set in form of a formal concept lattice. On the other hand, the theory of implications (dependencies between attributes) valid in a given formal context can be axiomatized in a sound and complete manner by the so-called canonical base, which furthermore contains a minimal number of implications w.r.t. the properties of soundness and completeness.
In spite of the different notions used in FCA and in DLs, there has been a very fruitful interaction between these two research areas. My thesis continues this line of research and, more specifically, I will describe how methods from FCA can be used to support the automatic construction and extension of DL ontologies from data
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