Dealing With Inconsistencies In DL-Lite Ontologies

As the increasing growth of Web information, it is urgent that Web contents need to be understandable for computer so that computer can process Web contents automatically and meaningfully. To solve this problem, Tim Berners-Lee first put forward the Semantic Web, which is an evolving extension of the World Wide Web in 1998. For Semantic Web, Web contents can be expressed not only by natural language, but also in a format that computer can read and use, thus computer can find Web sources automatically. Since the main aim of Semantic Web is that information can be shared and cooperated so that computers can interact each other, the shared knowledge with a standard format is needed.As an explicit specification of shared conceptualization, ontologies can define concepts and relations among them for one or more domains, so that concepts and relations among them can have explicit, unique definitions that people can accept in a shared knowledge base. So ontologies play an important role in Semantic Web. It is important to create, manage and maintain ontologies with high quality.However, ontologies may be created by distribution, multi-authorship, or different data sources. All these characteristics may introduce inconsistencies. Also, the reuse, merging or further extension of ontologies may result in inconsistencies in ontologies. When in-consistency occurs, the classical entailment in logics is explosive:any formula is a logical consequence of a contradiction. Therefore, conclusions drawn from an inconsistent ontology by classical logic inference may be completely meaningless. So it is essential to study how to deal with inconsistent ontologies.So far, most existing approaches mainly focus on expressive description logics (DL) which suffer from worst-case exponential time behavior of reasoning. As an important tractable DL family, DL-Lite can keep all the reasoning tasks tractable, in particular, with polynomial time complexity with respect to the size of the ontology. In this paper, we focus on DL-Lite and discuss how to deal with inconsistencies of Semantic Web ontologies. We mainly provide solutions to inconsistency debugging, paraconsistent query answering, and inconsistency measuring. Our contributions include the following points:(1) Inconsistency Diagnosis After analyzing some features of unsatisfiable concepts or unsatisfiable roles in DL-Lite, we present a novel algorithm for computing all minimal unsatisfiability-preserving sub-TBox (MUPS) of an ontology for an unsatisfiable con-cept or role in a DL-Lite ontology. We also present a comparison of our algorithm with another representative algorithm. The results indicate that the proposed algorithm is effecient and has an advantage over the previous work.(2) Paraconsistent Query Answering We propose to paraconsitent conjunctive query an-swering (CQA) in DL-Lite and extend the classical framework of query answering over DL-Lite ontologies to a three-valued semantics framework. We present a novel algorithm for paraconsistent query answering over DL-Lite and show that its compu-tational complexity is LOGSPACE in the size of the ABox.(3) Measuring inconsistency degrees of ontologies We propose a fine-gained approach to measuring inconsistency degrees of DL-Lite ontologies based on three-valued se-mantics. For a DL-Lite ontology, we show that it is desirable to consider all individ-uals, ABox and the negative inclusion closure of TBox to measure inconsistency and use them to define an inconsistency degree of a DL-Lite ontology. We present a pre-cise algorithm to compute the proposed inconsistency degree of a DL-Lite ontology and show that it is polynomial with respect to the size of the whole ontology. Unlike the approach that adopts a sequence of values to measure inconsistency in other pa-pers, we define a single value to measure inconsistency of a DL-Lite ontology which is more intuitive to be used as an inconsistency degree than a sequence of values.(4) Measuring inconsistency degrees of membership assertions The inconsistency de-gree of ontologies represents the contradiction that the whole ontology contains. How-ever, it can not tell us that which axiom assertions lead to inconsistency. In order to find the cause of inconsistency, we propose to measure inconsistency for membership assertions. We first give a definition of an inconsistency degree for membership asser-tions in DL-Lite ontologies. Then we present an algorithm to measure inconsistency for membership assertions and show that it is polynomial with respect to the size of the whole ontology.