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Named after the names of their proponents, Alchourron, Gardenfors, and Makinson.
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BRIEF SURVEY OF CAUSES FOR INCONSISTENCY IN THE SEMANTIC WEB
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5.2.4. Synthesis
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Various approaches discussed above (Marquies paraconsistent logic and Chopra s local belief revision) depending on syntactic selection procedures for extending the approximation set. Our approach borrows some ideas from Schaerf and Cadoli s approximation approach, Marquis and Porquet s paraconsistent reasoning approach, and Chopra, Parikh, and Wassermann s relevance approach. However, our main idea is relatively simple: given a selection function, which can be de ned on the syntactic or semantic relevance, like those have been used in computational linguistics, we select some consistent subtheory from an inconsistent ontology. Then we apply standard reasoning on the selected subtheory to nd meaningful answers. If a satisfying answer cannot be found, the relevance degree of the selection function is made less restrictive (see later sections for precise de nitions of these notions) thereby extending the consistent subtheory for further reasoning.
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5.3. BRIEF SURVEY OF CAUSES FOR INCONSISTENCY IN THE SEMANTIC WEB
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In the Semantic Web, inconsistencies may easily occur, sometimes even in small ontologies. Here are several scenarios which may cause inconsistencies:
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5.3.1. Inconsistency by Mis-representation of Default
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When a knowledge engineer speci es an ontology statement, she/he has to check carefully that the new statement is consistent, not only with respect to existing statements, but also with respect to statements that may be added in the future, which of course may not always be known at that moment. This makes it very dif cult to maintain consistency in ontology speci cations. Just consider a situation in which a knowledge engineer wants to create an ontology about animals:2 Bird v Animal Bird v Fly (Birds are animals), (Birds are ying animals).
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Although the knowledge engineer may realize that birds can y is not generally valid, he still wants to add it if he does not nd any counterexample in the current knowledge base because ying is one of
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2 Since we are dealing with (simple) ontological examples, we will adopt the notation from Description Logic, underlying the OWL language.
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REASONING WITH INCONSISTENT ONTOLOGIES
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the main features of birds. An ontology about birds without talking about ying is not satisfactory. Later on, one may want to extend the ontology with the following statements: Eagle v Bird (Eagles are birds), Penguin v Bird (Penguins are birds), Penguin v :Fly (Penguins are not ying animals). The concept Penguin in that ontology of birds is already unsatis able because it implies penguins can both y and not y. This would lead to an inconsistent ontology when there exists an instance of the concept Penguin. One may remove the axiom birds can y from the existing ontology to restore consistency. However, this approach is not reliable because of the following reasons: (a) it is hard to check that the removal would not cause any signi cant information loss in the current ontology, (b) one may not have the authority to remove statements which have been created in the current knowledge base, (c) it may be dif cult to know which part of the existing ontology can be removed if the knowledge base is very large. One would not blame the knowledge engineer for the creation of the axiom birds are ying animals at the beginning without considering future extensions because it is hard for the knowledge engineer to do so. One may argue that the current ontology languages and their counterparts in the Semantic Web cannot be used to handle this kind of problems because it requires nonmonotonic reasoning. The statement Birds can y has to be speci ed as a default. The ontology language OWL cannot deal with defaults. We have to wait for an extension of OWL to accommodate nonmonotonic logic. It is painful that we cannot talk about birds (that can y) and penguins (that cannot y) in the same ontology speci cation. An alternative approach is to divide the inconsistent ontology speci cation into multiple ontologies or modular ontologies to maintain their local consistency, like one that states birds can y, but does not talk about penguins, and another one that speci es penguins, but never mentions that birds can y. However, the problem for this approach is still the same as other ones. Again, an ontology about birds that cannot talk about both birds can y and penguins is not satisfactory. Another typical example is the MadCows ontolog3 in which MadCow is speci ed as a Cow which eats brains of sheep, whereas a Cow is considered as a vegetarian by default as follows: Cow v Vegetarian MadCow v Cow
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(Cows are vegetarians), (MadCows are cows),
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http://www.daml.org/ontologies/399
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