Ontology Module Extraction via Datalog Reasoning

Module extraction - the task of computing a (preferably small) fragment M of an ontology T that preserves entailments over a signature S - has found many applications in recent years. Extracting modules of minimal size is, however, computationally hard, and often algorithmically infeasible. Thus, practical techniques are based on approximations, where M provably captures the relevant entailments, but is not guaranteed to be minimal. Existing approximations, however, ensure that M preserves all second-order entailments of T w.r.t. S, which is stronger than is required in many applications, and may lead to large modules in practice. In this paper we propose a novel approach in which module extraction is reduced to a reasoning problem in datalog. Our approach not only generalises existing approximations in an elegant way, but it can also be tailored to preserve only specific kinds of entailments, which allows us to extract significantly smaller modules. An evaluation on widely-used ontologies has shown very encouraging results.Comment: 13 pages. To appear in AAAI-1

Modularity Through Inseparability : Algorithms, Extensions, and Evaluation

Module extraction is the task of computing, given a description logic ontology and a signature ∑ of interest, a subset (called a module) such that for certain applications that only concern ∑ the ontology can be equivalently replaced by the module. In most applications of module extraction it is desirable to compute a module which is as small as possible, and where possible a minimal one. In logic-based approaches to module extraction the most popular way to define modules is using inseparability relations, the strongest and most robust notion of this being model ∑-inseparability, where two ontologies are called ∑-inseparable iff the ∑-reducts of their models coincide. Then, a ∑-module is defined as a ∑-inseparable subset of the ontology. Unfortunately deciding if a subset of an ontology is a minimal ∑-module, over ontologies formulated in even moderately expressive logics, is of perpetually high complexity and often undecidable, and for this reason approximation algorithms are required. Instead of computing a minimal ∑-module one computes some ∑-module and the main research task is to minimise the size of these modules --- to compute an approximation of a minimal ∑-module. This thesis considers research surrounding approximations based on the model ∑-inseparability relation including: improving and extending existing approximation algorithms, providing a highly-optimised implementations, and the introduction a new methodology to evaluate just how well approximations approximate minimal modules, all supported by a significant empirical investigation

Games for query inseparability of description logic knowledge bases

We consider conjunctive query inseparability of description logic knowledge bases with respect to a given signature---a fundamental problem in knowledge base versioning, module extraction, forgetting and knowledge exchange. We give a uniform game-theoretic characterisation of knowledge base conjunctive query inseparability and develop worst-case optimal decision algorithms for fragments of Horn-ALCHI, including the description logics underpinning OWL 2 QL and OWL 2 EL. We also determine the data and combined complexity of deciding query inseparability. While query inseparability for all of these logics is P-complete for data complexity, the combined complexity ranges from P- to ExpTime- to 2ExpTime-completeness. We use these results to resolve two major open problems for OWL 2 QL by showing that TBox query inseparability and the membership problem for universal conjunctive query solutions in knowledge exchange are both ExpTime-complete for combined complexity. Finally, we introduce a more flexible notion of inseparability which compares answers to conjunctive queries in a given signature over a given set of individuals. In this case, checking query inseparability becomes NP-complete for data complexity, but the ExpTime- and 2ExpTime-completeness combined complexity results are preserved

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

Module-theoretic properties of reachability modules for SRIQ

Abstract. In this paper we investigate the module-theoretic properties of ⊥ − and ⊤-reachability modules in terms of inseparability relations for the DL SRIQ. We show that, although these modules are not depleting or self-contained, they share the robustness properties of syntactic locality modules and preserve all justifications for an entailment.