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REASONING WITH INCONSISTENT ONTOLOGIES
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MadCow
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Queries IA 50 50 42 36 50 48 254 236
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CA 0 4 0 16
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RA 0 2 2 0
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CIA 0 0 0 2
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IA Rate(%) 100 85.7 96 92.9
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ICR Rate(%) 100 100 100 99
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IA, intended answers; CA, cautious answers; RA, reckless answers; CIA, counter-intuitive answers; IA Rate, intended answers (%); ICR rate, IA+CA+RA (%).
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Figure 5.5 PION test results.
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Cows ontology is that many concepts which are intuitively disjoint (such as cows and sheep) are not actually declared as being disjoint (keep in mind that OWL has an open world semantics, and does not make the unique name assumption). As a result, many queries such as is the_cow a sheep are indeed undetermined on the basis of the ontology, and PION correctly reports them as undetermined. The average time cost of the tested queries is about 5 seconds even on a low-end PC (with 550 mHz CPU, 256 MB memory under Windows 2000). The counter-intuitive results occur in the MadCows Example. PION returns the accepted answer to the query is the_mad_cow a vegetarian This counter-intuitive answer results from the weakness of the syntactic relevance-based selection function because it always prefers a shorter relevance path when a con ict occurs. In the mad cow example, the path mad cow cow vegetarian is shorter than the path mad cow .eat brain eat bodypart sheep are animals eat animal NOT vegetarian. Therefore, the syntactic relevance-based selection function nds a consistent subtheory by simply ignoring the fact sheep are animals. The problem results from the unbalanced speci cation between Cow and MadCow, in which Cow is directly speci ed as a vegetarian whereas there is no direct statement a MadCow is not a vegetarian. There are several alternative approaches to solve this kind of problems. One is to introduce the locality requirement. Namely, the selection function starts with a certain subtheory which must always be selected. For example, the statement sheep are animals can be considered to be a knowledge statement which cannot be ignored. Another approach is to add a shortcut path, like the path mad cow eat animal NOT vegetarian to achieve the relevance balance between the concepts vegetarian and NOT vegetarian, as shown in the second mad cow example of PION testbed. The latter approach can be achieved automatically by accommodation of the semantic relevance from the user queries. The hypothesis is that both concepts appear in a query more frequently, when they are semantically more relevant. Therefore, from a semantic point of view, we can add a relevance shortcut path between strongly relevant concepts.
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DISCUSSION AND CONCLUSIONS
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5.8.3. Future Experiments
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As noted in many surveys of current Semantic Web work, most Semantic Web applications to date (including those included in this volume) use rather lightweight ontologies. These lightweight ontologies are often expressed in RDF Schema, which means that by de nition they will not contain any inconsistencies. However, closer inspection by Schlobach (2005a) revealed that such lightweight ontologies contain many implicit assumptions (such as disjointness of siblings in the class hierarchy) that have not been modeled explicitly because of the limitations of the lightweight representation language Schlobach s (2005a) study reveals that after making such implicit disjointness assumptions explicit (a process called semantic clari cation), many of the ontologies do reveal internal inconsistencies. In future experiments, we intend to determine to which extent it is still possible to locally reason in such semantically clari ed inconsistent ontologies using the heuristics described in this chapter.
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5.9. DISCUSSION AND CONCLUSIONS
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In this chapter, we have presented a framework for reasoning with inconsistent ontologies. We have introduced the formal de nitions of the selection functions, and investigated the strategies of inconsistency reasoning processing based on a linear extension strategy. One of the novelties of our approach is that the selection functions depend on individual queries. Our approach differs from the traditional one in paraconsistent reasoning, nonmonotonic reasoning, and belief revision, in which a pre-de ned preference ordering for all of the queries is required. This makes our approach more exible, and less inef cient to obtain intended results. The selection functions can be viewed as ones creating query-speci c preference orderings. We have implemented and presented a prototype of PION. In this chapter, we have provided the evaluation report of the prototype by applying it to the several inconsistent ontology examples. The tests show that our approach can obtain intuitive results in most cases for reasoning with inconsistent ontologies. Considering the fact that standard reasoners always result in either meaningless answers or incoherence errors for queries on inconsistent ontologies, we can claim that PION can do much better because it can provide a lot of intuitive, thus meaningful answers. This is a surprising result given the simplicity of our selection function. We are also working on a framework for inconsistent ontology diagnosis and repair by de ning a number of new nonstandard reasoning services to explain inconsistencies through pinpointing (Schlobach and Huang, 2005). An informed bottom-up approach to calculate
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