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Pons A, Keller R. 1997. Schema evolution in object databases by catalogs. Proceedings of the International Database Engineering and Applications Symposium (IDEAS 97), pp 368 376. Staab S, Studer R (Eds). 2004. Handbook on Ontologies. Springer: Heidelberg. Stojanovic L. 2004. Methods and Tools for Ontology Evolution. PhD thesis, University of Karlsruhe. Stojanovic L, Madche A, Motik B, Stojanovic N. 2002. User-driven ontology evolution management. In Proceedings of the European Conference of Knowledge Engineering and Management (EKAW 2002), Vol. 2473 of LNCS/LNAI, Springer. Stojanovic L, Maedche A, Stojanovic N, Studer R. 2003a. Ontology evolution as recon guration-design problem solving. In Proceedings of KCAP 2003, ACM, pp 162 171. Stojanovic L, Stojanovic N, Gonzalez J, Studer R. 2003b. OntoManager A System for the usage-based Ontology Management. In Proceedings of the CoopIS/DOA/ ODBASE 2003 Conference, Vol. 2888 of LNCS, Springer, pp 858 875. Sure Y, Erdmann M, Angele J, Staab S, Studer R, Wenke D. 2002a. OntoEdit: Collaborative ontology Engineering for the Semantic Web. In Proceedings of the First International Semantic Web Conference 2002 (ISWC 2002), Vol. 2342 of LNCS, Springer, pp 221 235. Sure Y, Staab S, Studer R. 2002b. Methodology for development and employment of ontology based knowledge management applications. SIGMOD Record, 31(4):18 23. Sure Y, Studer R. 2005. Semantic web technologies for digital libraries. Library Management 26(4/5):190 195. Tempich C, Pinto HS, Sure Y, Staab S. 2005. An Argumentation Ontology for DIstributed, Loosely-controlled and evolvInG Engineering processes of oNTologies (DILIGENT). In Proceedings of the Second European Semantic Web Conference (ESWC 2005), Vol. 3532 of LNCS, Springer, pp 241 256.
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Reasoning With Inconsistent Ontologies: Framework, Prototype, and Experiment
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Classical logical inference engines assume the consistency of the ontologies they reason with. Conclusions drawn from an inconsistent ontology by classical inference may be completely meaningless. An inconsistency reasoner is one which is able to return meaningful answers to queries, given an inconsistent ontology. In this chapter, we propose a general framework for reasoning with inconsistent ontologies. We present the formal de nitions of soundness, meaningfulness, local completeness, and maximality of an inconsistency reasoner. We propose and investigate a pre-processing algorithm, discuss the strategies of inconsistency reasoning based on pre-de ned selection functions dealing with concept relevance. We have implemented a system called PION (Processing Inconsistent ONtologies) for reasoning with inconsistent ontologies. We discuss how the syntactic relevance can be used for PION. In this chapter, we also report the preliminary experiments with PION.
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5.1. INTRODUCTION
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The Semantic Web is characterized by scalability, distribution, and joint author-ship. All these characteristics may introduce inconsistencies.
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This chapter is an extended and revised version of the paper Reasoning with Inconsistent Ontologies appeared in the Proceedings of the 19th Joint Conference on Arti cial Intelligence (IJCAI 05), 2005, pp 454 459.
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Semantic Web Technologies: Trends and Research in Ontology-based Systems John Davies, Rudi Studer, Paul Warren # 2006 John Wiley & Sons, Ltd
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REASONING WITH INCONSISTENT ONTOLOGIES
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Limiting the language expressivity with respect to negation (such as RDF and RDF Schema, which do not include negation) can avoid inconsistencies to a certain extent. However, the expressivity of these languages is too limited for many applications. In particular, OWL is already capable of expressing inconsistencies (McGuinness and van Harmelen, 2004). There are two main ways to deal with inconsistency. One is to diagnose and repair it when we encounter inconsistencies. Schlobach and Cornet (2003) propose a nonstandard reasoning service for debugging inconsistent terminologies. This is a possible approach, if we are dealing with one ontology and we would like to improve this ontology. Another approach is to simply live with the inconsistency and to apply a nonstandard reasoning method to obtain meaningful answers. In this chapter, we will focus on the latter, which is more suitable for the setting in the web area. For example, in a typical Semantic Web setting, one would be importing ontologies from other sources, making it impossible to repair them. Also the scale of the combined ontologies may be too large to make repair effective. Logical entailment is the inference relation that speci es which consequences can be drawn from a logical theory. A logical theory is inconsistent if it contains a contradiction: for some speci c statement A, both A and its negation not A are consequences of the theory. As is well known, the classical entailment in logics is explosive: any formula is a logical consequence of a contradiction. Therefore, conclusions drawn from an inconsistent knowledge base by classical inference may be completely meaningless. In this chapter, we propose a general framework for reasoning with inconsistent ontologies. We investigate how a reasoner with inconsistent ontologies can be developed for the Semantic Web. The general task of a reasoner with inconsistent ontologies is: given an inconsistent ontology, the reasoner should return meaningful answers to queries. In Section 5.4, we will provide a formal de nition about meaningfulness. This chapter is organized as follows: Section 5.2 discusses existing general approaches to reasoning with inconsistency. Section 5.3 overviews inconsistency in the Semantic Web by examining several typical examples and scenarios. Section 5.4 proposes a general framework of reasoning with inconsistent ontologies. A crucial element of this framework is so-called selection functions. Section 5.5 examines selection functions which are based on concept relevance. Section 5.6 presents the strategies and algorithms for processing inconsistent ontologies. Section 5.7 investigates how a selection function can be developed by a syntactic relevance relation. Section 5.8 describes a prototype of PION and report the experiments with PION. Section 5.9 discusses further work and concludes the chapter.
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