Rewriting Guarded Existential Rules into Small Datalog Programs

The goal of this paper is to understand the relative expressiveness of the query language in which queries are specified by a set of guarded (disjunctive) tuple-generating dependencies (TGDs) and an output (or \u27answer\u27) predicate. Our main result is to show that every such query can be translated into a polynomially-sized (disjunctive) Datalog program if the maximal number of variables in the (disjunctive) TGDs is bounded by a constant. To overcome the challenge that Datalog has no direct means to express the existential quantification present in TGDs, we define a two-player game that characterizes the satisfaction of the dependencies, and design a Datalog query that can decide the existence of a winning strategy for the game. For guarded disjunctive TGDs, we can obtain Datalog rules with disjunction in the heads. However, the use of disjunction is limited, and the resulting rules fall into a fragment that can be evaluated in deterministic single exponential time. We proceed quite differently for the case when the TGDs are not disjunctive and we show that we can obtain a plain Datalog query. Notably, unlike previous translations for related fragments, our translation requires only polynomial time if the maximal number of variables in the (disjunctive) TGDs is bounded by a constant

A data complexity and rewritability tetrachotomy of ontology-mediated queries with a covering axiom

Aiming to understand the data complexity of answering conjunctive queries mediated by an axiom stating that a class is covered by the union of two other classes, we show that deciding their first-order rewritability is PSPACE-hard and obtain a number of sufficient conditions for membership in AC0, L, NL, and P. Our main result is a complete syntactic AC0/NL/P/CONP tetrachotomy of path queries under the assumption that the covering classes are disjoint

Conjunctive query answering over unrestricted OWL 2 ontologies

Conjunctive Query (CQ) answering is a primary reasoning task over knowledge bases. However, when considering expressive description logics, query answering can be computationally very expensive; reasoners for CQ answering, although heavily optimized, often sacrifice expressive power of the input ontology or completeness of the computed answers in order to achieve tractability and scalability for the problem. In this work, we present a hybrid query answering architecture that combines various services to provide a CQ answering service for OWL. Specifically, it combines scalable CQ answering services for tractable languages with a CQ answering service for a more expressive language approaching the full OWL 2. If the query can be fully answered by one of the tractable services, then that service is used, to ensure maximum performance. Otherwise, the tractable services are used to compute lower and upper bound approximations. The union of the lower bounds and the intersection of the upper bounds are then compared. If the bounds do not coincide, then the “gap” answers are checked using the “full” service. These techniques led to the development of two new systems: (i) RSAComb, an efficient implementation of a new tractable answering service for RSA (role safety acyclic) (ii) ACQuA, a reference implementation of the proposed hybrid architecture combining RSAComb, PAGOdA, and HermiT to provide a CQ answering service for OWL. Our extensive evaluation shows how the additional computational cost introduced by reasoning over a more expressive language like RSA can still provide a significant improvement compared to relying on a fully-fledged reasoner. Additionally, we show how ACQuA can reliably match the performance of PAGOdA, a state-of-the-art CQ answering system that uses a similar approach, and can significantly improve performance when PAGOdA extensively relies on the underlying fully-fledged reasoner

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

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas