Explaining Query Answers under Inconsistency-Tolerant Semantics over Description Logic Knowledge Bases (Extended Abstract)

The problem of querying description logic (DL) knowledge bases (KBs) using database-style queries (in particular, conjunctive queries) has been a major focus of recent DL research. Since scalability is a key concern, much of the work has focused on lightweight DLs for which query answering can be performed in polynomial time w.r.t. the size of the ABox. The DL-Lite family of lightweight DLs [10] is especially popular due to the fact that query answering can be reduced, via query rewriting, to the problem of standard database query evaluation. Since the TBox is usually developed by experts and subject to extensive debugging, it is often reasonable to assume that its contents are correct. By contrast, the ABox is typically substantially larger and subject to frequent modifications, making errors almost inevitable. As such errors may render the KB inconsistent, several inconsistency-tolerant semantics have been introduced in order to provide meaningful answers to queries posed over inconsistent KBs. Arguably the most well-known is the AR semantics [17], inspired by work on consistent query answering in databases (cf. [4] for a survey). Query answering under AR semantics amounts to considering those answers (w.r.t. standard semantics) that can be obtained from every repair, the latter being defined as an inclusion-maximal subset of the ABox that is consistent with the TBox. A more cautious semantics, called IAR semantics The need to equip reasoning systems with explanation services is widely acknowledged by the DL community. Indeed, there have been numerous works on axiom pinpointing, in which the objective is to identify (minimal) subsets of a KB that entail a given TBox axiom (or ABox assertion

Reasoning in inconsistent prioritized knowledge bases: an argumentative approach

A study of query answering in prioritized ontological knowledge bases (KBs) has received attention in recent years. While several semantics of query answering have been proposed and their complexity is rather well-understood, the problem of explaining inconsistency-tolerant query answers has paid less attention. Explaining query answers permits users to understand not only what is entailed or not entailed by an inconsistent DL-LiteR KBs in the presence of priority, but also why. We, therefore, concern with the use of argumentation frameworks to allow users to better understand explanation techniques of querying answers over inconsistent DL-LiteR KBs in the presence of priority. More specifically, we propose a new variant of Dung’s argumentation frameworks, which corresponds to a given inconsistent DL-LiteR KB. We clarify a close relation between preferred subtheories adopted in such prioritized DL-LiteR setting and acceptable semantics of the corresponding argumentation framework. The significant result paves the way for applying algorithms and proof theories to establish preferred subtheories inferences in prioritized DL-LiteR KBs

Inconsistency-tolerant Query Answering in Ontology-based Data Access

Ontology-based data access (OBDA) is receiving great attention as a new paradigm for managing information systems through semantic technologies. According to this paradigm, a Description Logic ontology provides an abstract and formal representation of the domain of interest to the information system, and is used as a sophisticated schema for accessing the data and formulating queries over them. In this paper, we address the problem of dealing with inconsistencies in OBDA. Our general goal is both to study DL semantical frameworks that are inconsistency-tolerant, and to devise techniques for answering unions of conjunctive queries under such inconsistency-tolerant semantics. Our work is inspired by the approaches to consistent query answering in databases, which are based on the idea of living with inconsistencies in the database, but trying to obtain only consistent information during query answering, by relying on the notion of database repair. We first adapt the notion of database repair to our context, and show that, according to such a notion, inconsistency-tolerant query answering is intractable, even for very simple DLs. Therefore, we propose a different repair-based semantics, with the goal of reaching a good compromise between the expressive power of the semantics and the computational complexity of inconsistency-tolerant query answering. Indeed, we show that query answering under the new semantics is first-order rewritable in OBDA, even if the ontology is expressed in one of the most expressive members of the DL-Lite family

Complexity of Approximate Query Answering under Inconsistency in Datalog+/-

This is the author accepted manuscript. The final version is freely available from IJCAI via the link in this recordSeveral semantics have been proposed to query inconsistent ontological knowledge bases, including the intersection of repairs and the intersection of closed repairs as two approximate inconsistencytolerant semantics. In this paper, we analyze the complexity of conjunctive query answering under these two semantics for a wide range of Datalog± languages. We consider both the standard setting, where errors may only be in the database, and the generalized setting, where also the rules of a Datalog± knowledge base may be erroneous.This work was supported by The Alan Turing Institute under the UK EPSRC grant EP/N510129/1, and by the EPSRC grants EP/R013667/1, EP/L012138/1, and EP/M025268/1

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

Querying and Repairing Inconsistent Prioritized Knowledge Bases: Complexity Analysis and Links with Abstract Argumentation

In this paper, we explore the issue of inconsistency handling over prioritized knowledge bases (KBs), which consist of an ontology, a set of facts, and a priority relation between conflicting facts. In the database setting, a closely related scenario has been studied and led to the definition of three different notions of optimal repairs (global, Pareto, and completion) of a prioritized inconsistent database. After transferring the notions of globally-, Pareto- and completion-optimal repairs to our setting, we study the data complexity of the core reasoning tasks: query entailment under inconsistency-tolerant semantics based upon optimal repairs, existence of a unique optimal repair, and enumeration of all optimal repairs. Our results provide a nearly complete picture of the data complexity of these tasks for ontologies formulated in common DL-Lite dialects. The second contribution of our work is to clarify the relationship between optimal repairs and different notions of extensions for (set-based) argumentation frameworks. Among our results, we show that Pareto-optimal repairs correspond precisely to stable extensions (and often also to preferred extensions), and we propose a novel semantics for prioritized KBs which is inspired by grounded extensions and enjoys favourable computational properties. Our study also yields some results of independent interest concerning preference-based argumentation frameworks.Comment: 27 pages. To appear in the 17th International Conference on Principles of Knowledge Representation and Reasoning (KR 2020) without the appendi

Dealing with Inconsistencies and Updates in Description Logic Knowledge Bases

The main purpose of an "Ontology-based Information System" (OIS) is to provide an explicit description of the domain of interest, called ontology, and let all the functions of the system be based on such representation, thus freeing the users from the knowledge about the physical repositories where the real data reside. The functionalities that an OIS should provide to the user include both query answering, whose goal is to extract information from the system, and update, whose goal is to modify the information content of the system in order to reflect changes in the domain of interest. The "ontology" is a formal, high quality intentional representation of the domain, designed in such a way to avoid inconsistencies in the modeling of concepts and relationships. On the contrary, the extensional level of the system, constituted by a set of autonomous, heterogeneous data sources, is built independently from the conceptualization represented by the ontology, and therefore may contain information that is incoherent with the ontology itself. This dissertation presents a detailed study on the problem of dealing with inconsistencies in OISs, both in query answering, and in performing updates. We concentrate on the case where the knowledge base in the OISs is expressed in Description Logics, especially the logics of the DL-lite family. As for query answering, we propose both semantical frameworks that are inconsistency-tolerant, and techniques for answering unions of conjunctive queries posed to OISs under such inconsistency-tolerant semantics. As for updates, we present an approach to compute the result of updating a possibly inconsistent OIS with both insertion and deletion of extensional knowledge

Federated knowledge base debugging in DL-Lite A

Due to the continuously growing amount of data the federation of different and distributed data sources gained increasing attention. In order to tackle the challenge of federating heterogeneous sources a variety of approaches has been proposed. Especially in the context of the Semantic Web the application of Description Logics is one of the preferred methods to model federated knowledge based on a well-defined syntax and semantics. However, the more data are available from heterogeneous sources, the higher the risk is of inconsistency – a serious obstacle for performing reasoning tasks and query answering over a federated knowledge base. Given a single knowledge base the process of knowledge base debugging comprising the identification and resolution of conflicting statements have been widely studied while the consideration of federated settings integrating a network of loosely coupled data sources (such as LOD sources) has mostly been neglected. In this thesis we tackle the challenging problem of debugging federated knowledge bases and focus on a lightweight Description Logic language, called DL-LiteA, that is aimed at applications requiring efficient and scalable reasoning. After introducing formal foundations such as Description Logics and Semantic Web technologies we clarify the motivating context of this work and discuss the general problem of information integration based on Description Logics. The main part of this thesis is subdivided into three subjects. First, we discuss the specific characteristics of federated knowledge bases and provide an appropriate approach for detecting and explaining contradictive statements in a federated DL-LiteA knowledge base. Second, we study the representation of the identified conflicts and their relationships as a conflict graph and propose an approach for repair generation based on majority voting and statistical evidences. Third, in order to provide an alternative way for handling inconsistency in federated DL-LiteA knowledge bases we propose an automated approach for assessing adequate trust values (i.e., probabilities) at different levels of granularity by leveraging probabilistic inference over a graphical model. In the last part of this thesis, we evaluate the previously developed algorithms against a set of large distributed LOD sources. In the course of discussing the experimental results, it turns out that the proposed approaches are sufficient, efficient and scalable with respect to real-world scenarios. Moreover, due to the exploitation of the federated structure in our algorithms it further becomes apparent that the number of identified wrong statements, the quality of the generated repair as well as the fineness of the assessed trust values profit from an increasing number of integrated sources