Repairing Description Logic Ontologies by Weakening Axioms

The classical approach for repairing a Description Logic ontology O in the sense of removing an unwanted consequence α is to delete a minimal number of axioms from O such that the resulting ontology O´ does not have the consequence α. However, the complete deletion of axioms may be too rough, in the sense that it may also remove consequences that are actually wanted. To alleviate this problem, we propose a more gentle way of repair in which axioms are not necessarily deleted, but only weakened. On the one hand, we investigate general properties of this gentle repair method. On the other hand, we propose and analyze concrete approaches for weakening axioms expressed in the Description Logic EL

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

Two Approaches to Ontology Aggregation Based on Axiom Weakening

Axiom weakening is a novel technique that allows for fine-grained repair of inconsistent ontologies. In a multi-agent setting, integrating ontologies corresponding to multiple agents may lead to inconsistencies. Such inconsistencies can be resolved after the integrated ontology has been built, or their generation can be prevented during ontology generation. We implement and compare these two approaches. First, we study how to repair an inconsistent ontology resulting from a voting-based aggregation of views of heterogeneous agents. Second, we prevent the generation of inconsistencies by letting the agents engage in a turn-based rational protocol about the axioms to be added to the integrated ontology. We instantiate the two approaches using real-world ontologies and compare them by measuring the levels of satisfaction of the agents w.r.t. the ontology obtained by the two procedures

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

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Completing and Debugging Ontologies: state of the art and challenges

As semantically-enabled applications require high-quality ontologies, developing and maintaining ontologies that are as correct and complete as possible is an important although difficult task in ontology engineering. A key step is ontology debugging and completion. In general, there are two steps: detecting defects and repairing defects. In this paper we discuss the state of the art regarding the repairing step. We do this by formalizing the repairing step as an abduction problem and situating the state of the art with respect to this framework. We show that there are still many open research problems and show opportunities for further work and advancing the field.Comment: 56 page

Axiom Pinpointing

Axiom pinpointing refers to the task of finding the specific axioms in an ontology which are responsible for a consequence to follow. This task has been studied, under different names, in many research areas, leading to a reformulation and reinvention of techniques. In this work, we present a general overview to axiom pinpointing, providing the basic notions, different approaches for solving it, and some variations and applications which have been considered in the literature. This should serve as a starting point for researchers interested in related problems, with an ample bibliography for delving deeper into the details

Optimal Fixed-Premise Repairs of EL TBoxes: Extended Version

Reasoners can be used to derive implicit consequences from an ontology. Sometimes unwanted consequences are revealed, indicating errors or privacy-sensitive information, and the ontology needs to be appropriately repaired. The classical approach is to remove just enough axioms such that the unwanted consequences vanish. However, this is often too rough since mere axiom deletion also erases many other consequences that might actually be desired. The goal should not be to remove a minimal number of axioms but to modify the ontology such that only a minimal number of consequences is removed, including the unwanted ones. Specifically, a repair should rather be logically entailed by the input ontology, instead of being a subset. To this end, we introduce a framework for computing fixed-premise repairs of $\mathcal{EL}$ TBoxes. In the first variant the conclusions must be generalizations of those in the input TBox, while in the second variant no such restriction is imposed. In both variants, every repair is entailed by an optimal one and, up to equivalence, the set of all optimal repairs can be computed in exponential time. A prototypical implementation is provided. In addition, we show new complexity results regarding gentle repairs.This is an extended version of an article accepted at the 45th German Conference on Artificial Intelligence (KI 2022)

Datalog± Ontology Consolidation

Knowledge bases in the form of ontologies are receiving increasing attention as they allow to clearly represent both the available knowledge, which includes the knowledge in itself and the constraints imposed to it by the domain or the users. In particular, Datalog ± ontologies are attractive because of their property of decidability and the possibility of dealing with the massive amounts of data in real world environments; however, as it is the case with many other ontological languages, their application in collaborative environments often lead to inconsistency related issues. In this paper we introduce the notion of incoherence regarding Datalog± ontologies, in terms of satisfiability of sets of constraints, and show how under specific conditions incoherence leads to inconsistent Datalog ± ontologies. The main contribution of this work is a novel approach to restore both consistency and coherence in Datalog± ontologies. The proposed approach is based on kernel contraction and restoration is performed by the application of incision functions that select formulas to delete. Nevertheless, instead of working over minimal incoherent/inconsistent sets encountered in the ontologies, our operators produce incisions over non-minimal structures called clusters. We present a construction for consolidation operators, along with the properties expected to be satisfied by them. Finally, we establish the relation between the construction and the properties by means of a representation theorem. Although this proposal is presented for Datalog± ontologies consolidation, these operators can be applied to other types of ontological languages, such as Description Logics, making them apt to be used in collaborative environments like the Semantic Web.Fil: Deagustini, Cristhian Ariel David. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Martinez, Maria Vanina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Falappa, Marcelo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Simari, Guillermo Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; Argentin