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

A Bayesian Extension of the Description Logic ALC

Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. A probabilistic extension of a light-weight DL was recently proposed for dealing with certain knowledge occurring in uncertain contexts. In this paper, we continue that line of research by introducing the Bayesian extension BALC of the DL ALC. We present a tableau-based procedure for deciding consistency, and adapt it to solve other probabilistic, contextual, and general inferences in this logic. We also show that all these problems remain ExpTime-complete, the same as reasoning in the underlying classical ALC

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

Error-Tolerant Reasoning in the Description Logic EL

Developing and maintaining ontologies is an expensive and error-prone task. After an error is detected, users may have to wait for a long time before a corrected version of the ontology is available. In the meantime, one might still want to derive meaningful knowledge from the ontology, while avoiding the known errors. We study error-tolerant reasoning tasks in the description logic EL. While these problems are intractable, we propose methods for improving the reasoning times by precompiling information about the known errors and using proof-theoretic techniques for computing justifications. A prototypical implementation shows that our approach is feasible for large ontologies used in practice

Blending under deconstruction

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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

Towards Parallel Repair Using Decompositions

Ontology repair remains one of the main bottlenecks for the development of ontologies for practical use. Many automated methods have been developed for suggesting potential repairs, but ultimately human intervention is required for selecting the adequate one, and the human expert might be overwhelmed by the amount of information delivered to her. We propose a decomposition of ontologies into smaller components that can be repaired in parallel. We show the utility of our approach for ontology repair, provide algorithms for computing this decomposition through standard reasoning, and study the complexity of several associated problems