Repairing and reasoning with inconsistent and uncertain ontologies

Abstract

With the development of semantic web, the quality and correctness of ontologies play more and more important roles in semantic representation and knowledge sharing. However, ontologies are often inconsistent and uncertain in real situations. Because of the difficulty in ensuring the quality of ontologies, there is an increasing need for dealing with the inconsistency and uncertainty in real-world applications of ontological reasoning and management. This paper adopts two methods to handle the inconsistent and uncertain ontologies: the first one is to repair the inconsistency, algorithms RIO and RIUO are proposed to compute the candidate repair set, the consistency of ontology could be recovered through deleting or modifying the axioms in candidate repair set; the second one is to develop a non-standard reasoning method to obtain meaningful answers, algorithms RMU and RMIU are proposed to perform query-specific reasoning methods for inconsistent and uncertain ontologies without changing the original ontologies. Finally the prototype system is constructed and the experiment results validate the usability and effectiveness of our approaches.

Introduction

Ontologies play an important role in the Semantic Web [1]. The development of Semantic Web is highly dependent on the quality and correctness of ontologies. However, in real situations, ontologies are often inconsistent and uncertain.

An inconsistent ontology means that an error or a conflict exists in this ontology, as a result some concepts in the ontology cannot be interpreted correctly. The inconsistencies of ontologies may come from mis-presentation, polysemy, migration from another formalism, and integration from multiple sources. The inconsistency will result in wrong answers during ontology reasoning, and also result in false semantic understanding and knowledge representation.

Existing reasoners are able to detect inconsistencies in ontologies, however, there is relatively limited support for resolving the problems. Some researchers have already addressed this issue [2], [3], [4], [5], [6], but their methods are either low efficient in calculation or specific to certain domain, and cannot find all the solutions to repair the inconsistency. Accordingly, the ability to efficiently resolve the inconsistency and find a best solution is of utmost importance in ontological reasoning and management.

Additionally, sometimes ontologies have uncertainty. An uncertain ontology means that the correctness of the ontology is probabilistic. Without a means of expressing uncertainty we are unable to say much of what we know. There are mainly three sources of uncertain ontologies: (1) subjective uncertainty of experts when they build the ontologies, (2) the uncertainty from original ontologies when the ontology is integrated from several sub-ontologies, and (3) the uncertainty from (semi-) automatically ontology learning tools.

Existing methods [7], [8], [9], [10], [11] can reduce the uncertainty to some extent but cannot resolve this problem very well, especially when the inconsistency and uncertainty happen simultaneously. So the need for dealing with uncertainty in semantically aware systems also becomes a serious problem.

Because the inconsistent and uncertain ontologies widely exist in semantic web, and it is always very hard to ensure the quality of ontologies, this paper proposes two methods for dealing with inconsistent and uncertain ontologies.

The first one is to repair the error whenever an inconsistency is encountered. First the minimal inconsistent subset, extended error set and candidate repair set of the ontology are defined, then the algorithm RIO is presented to compute the candidate repair set. The consistency of ontology could be recovered efficiently through deleting or modifying the axioms in candidate repair set. Then the confidence of the ontology is further considered to measure how confident the user is of the correctness of the elements, and the algorithm RIUO is proposed to repair the inconsistency and uncertainty simultaneously.

The second method is to develop a non-standard reasoning method to obtain meaningful answers. Algorithm RMU is presented to reason with uncertain ontologies; algorithm RMIU is proposed to perform a query-specific reasoning method for inconsistent and uncertain ontologies without changing the original ontologies. The reasoning route and certainty degree of each answer are also provided to the user for facilitating his selection of the most credible answer.

The primary contributions of this paper are summarized as follows:

• Generally speaking, there is more than one solution that could recover the consistency of ontology. But existing methods cannot find all the solutions. Our methods compute the candidate repair sets that include all the possible solutions, also the best solution. Thus it is more convenient for the users to choose the most suitable solution according to their knowledge and specific scenario, and do analysis and make customized modifications.

• The reasoning methods for inconsistent and uncertain ontologies adopt an incrementally selection function, which is capable of selecting elements related to a specific query. Accordingly, the elements necessary for the reasoning could be obtained fast and the query results could be returned efficiently.

• The query results achieved by our method include not only “True” and “False” answers, but also the specific reasoning route (path) and certainty degree of each answer. In this way, the user may obtain more useful information to facilitate his selection of the most credible query result according to the certainty degree of each result.

• The empirical study of the proposed methods is reported. The prototype system constructs an ontology for testing and the evaluation results validate the usability and promise of our approaches.

The rest of the paper is organized as follows: Section 2 introduces relevant terms and definitions as preliminaries. Section 3 describes the algorithms RIO and RIUO for repairing inconsistent and uncertain ontologies. Section 4 presents the algorithms RMU and RMIU to reason with inconsistent and uncertain ontologies. The system implementation and experiment results are discussed in Section 5. Section 6 reviews the related work of inconsistent and uncertain ontology handling. Finally, the conclusions and future work are depicted in Section 7.