7 research outputs found
Living Without Beth and Craig: Definitions and Interpolants in Description Logics with Nominals and Role Inclusions
The Craig interpolation property (CIP) states that an interpolant for an
implication exists iff it is valid. The projective Beth definability property
(PBDP) states that an explicit definition exists iff a formula stating implicit
definability is valid. Thus, the CIP and PBDP transform potentially hard
existence problems into deduction problems in the underlying logic. Description
Logics with nominals and/or role inclusions do not enjoy the CIP nor PBDP, but
interpolants and explicit definitions have many potential applications in
ontology engineering and ontology-based data management. In this article we
show the following: even without Craig and Beth, the existence of interpolants
and explicit definitions is decidable in description logics with nominals
and/or role inclusions such as ALCO, ALCH and ALCHIO. However, living without
Craig and Beth makes this problem harder than deduction: we prove that the
existence problems become 2ExpTime-complete, thus one exponential harder than
validity. The existence of explicit definitions is 2ExpTime-hard even if one
asks for a definition of a nominal using any symbol distinct from that nominal,
but it becomes ExpTime-complete if one asks for a definition of a concept name
using any symbol distinct from that concept name.Comment: We have added results on description logics with role inclusions and
an ExpTime-completeness result for the explicit definability of concept
names. The title has been modified by adding role inclusions. This paper has
been accepted for AAAA 202
Games for query inseparability of description logic knowledge bases
We consider conjunctive query inseparability of description logic knowledge bases with respect to a given signature---a fundamental problem in knowledge base versioning, module extraction, forgetting and knowledge exchange. We give a uniform game-theoretic characterisation of knowledge base conjunctive query inseparability and develop worst-case optimal decision algorithms for fragments of Horn-ALCHI, including the description logics underpinning OWL 2 QL and OWL 2 EL. We also determine the data and combined complexity of deciding query inseparability. While query inseparability for all of these logics is P-complete for data complexity, the combined complexity ranges from P- to ExpTime- to 2ExpTime-completeness. We use these results to resolve two major open problems for OWL 2 QL by showing that TBox query inseparability and the membership problem for universal conjunctive query solutions in knowledge exchange are both ExpTime-complete for combined complexity. Finally, we introduce a more flexible notion of inseparability which compares answers to conjunctive queries in a given signature over a given set of individuals. In this case, checking query inseparability becomes NP-complete for data complexity, but the ExpTime- and 2ExpTime-completeness combined complexity results are preserved
Query inseparability for ALC ontologies
We investigate the problem whether two ALC ontologies are indistinguishable (or inseparable) by means of queries in
a given signature, which is fundamental for ontology engineering tasks such as ontology versioning, modularisation,
update, and forgetting. We consider both knowledge base (KB) and TBox inseparability. For KBs, we give model-theoretic
criteria in terms of (finite partial) homomorphisms and products and prove that this problem is undecidable
for conjunctive queries (CQs), but 2ExpTime-complete for unions of CQs (UCQs). The same results hold if (U)CQs are
replaced by rooted (U)CQs, where every variable is connected to an answer variable. We also show that inseparability
by CQs is still undecidable if one KB is given in the lightweight DL EL and if no restrictions are imposed on the
signature of the CQs. We also consider the problem whether two ALC TBoxes give the same answers to any query
over any ABox in a given signature and show that, for CQs, this problem is undecidable, too. We then develop
model-theoretic criteria for HornALC TBoxes and show using tree automata that, in contrast, inseparability becomes
decidable and 2ExpTime-complete, even ExpTime-complete when restricted to (unions of) rooted CQs
Knowledge base exchange: the case of OWLâ2âQL
In this article, we define and study the problem of exchanging knowledge between a source and a target knowledge base (KB), connected through mappings. Differently from the traditional database exchange setting, which considers only the exchange of data, we are interested in exchanging implicit knowledge. As representation formalism we use Description Logics (DLs), thus assuming that the source and target KBs are given as a DL TBox+ABox, while the mappings have the form of DL TBox assertions. We define a general framework of KB exchange, and study the problem of translating the knowledge in the source KB according to the mappings expressed in OWLâ2âQL, the profile of the standard Web Ontology Language OWL 2 based on the description logic DL-LiteR. We develop novel game- and automata-theoretic techniques, and we provide complexity results that range from NLogSpace to ExpTim
Reasoning in Description Logic Ontologies for Privacy Management
A rise in the number of ontologies that are integrated and distributed in numerous application systems may provide the users to access the ontologies with different privileges and purposes. In this situation, preserving confidential information from possible unauthorized disclosures becomes a critical requirement. For instance, in the clinical sciences, unauthorized disclosures of medical information do not only threaten the system but also, most importantly, the patient data. Motivated by this situation, this thesis initially investigates a privacy problem, called the identity problem, where the identity of (anonymous) objects stored in Description Logic ontologies can be revealed or not. Then, we consider this problem in the context of role-based access control to ontologies and extend it to the problem asking if the identity belongs to a set of known individuals of cardinality smaller than the number k. If it is the case that some confidential information of persons, such as their identity, their relationships or their other properties, can be deduced from an ontology, which implies that some privacy policy is not fulfilled, then one needs to repair this ontology such that the modified one complies with the policies and preserves the information from the original ontology as much as possible. The repair mechanism we provide is called gentle repair and performed via axiom weakening instead of axiom deletion which was commonly used in classical approaches of ontology repair. However, policy compliance itself is not enough if there is a possible attacker that can obtain relevant information from other sources, which together with the modified ontology still violates the privacy policies. Safety property is proposed to alleviate this issue and we investigate this in the context of privacy-preserving ontology publishing. Inference procedures to solve those privacy problems and additional investigations on the complexity of the procedures, as well as the worst-case complexity of the problems, become the main contributions of this thesis.:1. Introduction
1.1 Description Logics
1.2 Detecting Privacy Breaches in Information System
1.3 Repairing Information Systems
1.4 Privacy-Preserving Data Publishing
1.5 Outline and Contribution of the Thesis
2. Preliminaries
2.1 Description Logic ALC
2.1.1 Reasoning in ALC Ontologies
2.1.2 Relationship with First-Order Logic
2.1.3. Fragments of ALC
2.2 Description Logic EL
2.3 The Complexity of Reasoning Problems in DLs
3. The Identity Problem and Its Variants in Description Logic Ontologies
3.1 The Identity Problem
3.1.1 Description Logics with Equality Power
3.1.2 The Complexity of the Identity Problem
3.2 The View-Based Identity Problem
3.3 The k-Hiding Problem
3.3.1 Upper Bounds
3.3.2 Lower Bound
4. Repairing Description Logic Ontologies
4.1 Repairing Ontologies
4.2 Gentle Repairs
4.3 Weakening Relations
4.4 Weakening Relations for EL Axioms
4.4.1 Generalizing the Right-Hand Sides of GCIs
4.4.2 Syntactic Generalizations
4.5 Weakening Relations for ALC Axioms
4.5.1 Generalizations and Specializations in ALC w.r.t. Role Depth
4.5.2 Syntactical Generalizations and Specializations in ALC
5. Privacy-Preserving Ontology Publishing for EL Instance Stores
5.1 Formalizing Sensitive Information in EL Instance Stores
5.2 Computing Optimal Compliant Generalizations
5.3 Computing Optimal Safe^{\exists} Generalizations
5.4 Deciding Optimality^{\exists} in EL Instance Stores
5.5 Characterizing Safety^{\forall}
5.6 Optimal P-safe^{\forall} Generalizations
5.7 Characterizing Safety^{\forall\exists} and Optimality^{\forall\exists}
6. Privacy-Preserving Ontology Publishing for EL ABoxes
6.1 Logical Entailments in EL ABoxes with Anonymous Individuals
6.2 Anonymizing EL ABoxes
6.3 Formalizing Sensitive Information in EL ABoxes
6.4 Compliance and Safety for EL ABoxes
6.5 Optimal Anonymizers
7. Conclusion
7.1 Main Results
7.2 Future Work
Bibliograph