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

Query Answer Explanations under Existential Rules

Ontology-mediated query answering is an extensively studied paradigm, which aims at improving query answers with the use of a logical theory. In this paper, we focus on ontology languages based on existential rules, and we carry out a thorough complexity analysis of the problem of explaining query answers in terms of minimal subsets of database facts and related task

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

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

Semiring Provenance for Lightweight Description Logics

We investigate semiring provenance--a successful framework originally defined in the relational database setting--for description logics. In this context, the ontology axioms are annotated with elements of a commutative semiring and these annotations are propagated to the ontology consequences in a way that reflects how they are derived. We define a provenance semantics for a language that encompasses several lightweight description logics and show its relationships with semantics that have been defined for ontologies annotated with a specific kind of annotation (such as fuzzy degrees). We show that under some restrictions on the semiring, the semantics satisfies desirable properties (such as extending the semiring provenance defined for databases). We then focus on the well-known why-provenance, which allows to compute the semiring provenance for every additively and multiplicatively idempotent commutative semiring, and for which we study the complexity of problems related to the provenance of an axiom or a conjunctive query answer. Finally, we consider two more restricted cases which correspond to the so-called positive Boolean provenance and lineage in the database setting. For these cases, we exhibit relationships with well-known notions related to explanations in description logics and complete our complexity analysis. As a side contribution, we provide conditions on an ELHI_bot ontology that guarantee tractable reasoning.Comment: Paper currently under review. 102 page

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

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