77 research outputs found
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
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
Concise Justifications Versus Detailed Proofs for Description Logic Entailments
We discuss explanations in Description Logics (DLs), a family of logics used for knowledge representation. Initial work on explaining consequences for DLs had focused on justifications, which are minimal subsets of axioms that entail the consequence. More recently, it was proposed that proofs can provide more detailed information about why a consequence follows. Moreover, several measures have been proposed to estimate the comprehensibility of justifications and proofs, for example, their size or the complexity of logical expressions. In this paper, we analyze the connection between these measures, e.g. whether small justifications necessarily give rise to small proofs. We use a dataset of DL proofs that was constructed last year based on the ontologies of the OWL Reasoner Evaluation 2015. We find that, in general, less complex justifications indeed correspond to less complex proofs, and discuss some exceptions to this rule
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
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
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
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