Iterated applications of belief change operators are essential for different scenarios such as that of ontology evolution where new information is not presented at once but only in piecemeal fashion within a sequence. I discuss iterated applications of so called reinterpretation operators that trace conflicts between ontologies back to the ambiguous of symbols and that provide conflict resolution strategies with bridging axioms. The discussion centers on adaptations of the classical iteration postulates according to Darwiche and Pearl. The main result of the paper is that reinterpretation operators fulfill the postulates for sequences containing only atomic triggers. For complex triggers, a fulfillment is not guaranteed and indeed there are different reasons for the different postulates why they should not be fulfilled in the particular scenario of ontology revision with well developed ontologies.
Bridging axioms are special mappings that are used in the reinterpretation operator as auxiliary means to implement ontology revision. One may also consider mappings by themselves as the objects of revision @cite_8 @cite_15 . A particularly interesting case of mapping revision comes into play with mappings used in the ontology based data access paradigm @cite_0 . These mappings are meant to lift data from relational DBs to the ontology level thereby mapping between close world of data and the open world of ontologies. In this setting different forms of inconsistencies induced by the mappings can be defined (such as local vs. global inconsistency) and based on this mapping evolution ensuring (one form of consistency) be investigated @cite_16 .
@cite_0 @cite_15 @cite_16 @cite_8
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Ontology matching is one of the key research topics in the field of the Semantic Web. There are many matching systems that generate mappings between different ontologies either automatically or semi-automatically. However, the mappings generated by these systems may be inconsistent with the ontologies. Several approaches have been proposed to deal with the inconsistencies between mappings and ontologies. This problem is often called a mapping revision problem, as the ontologies are assumed to be correct, whereas the mappings are repaired when resolving the inconsistencies. In this paper, we first propose a conflict-based mapping revision operator and show that it can be characterized by two logical postulates adapted from some existing postulates for belief base revision. We then provide an algorithm for iterative mapping revision by using an ontology revision operator and show that this algorithm defines a conflict-based mapping revision operator. Three concrete ontology revision operators are given to instantiate the iterative algorithm, which result in three different mapping revision algorithms. We implement these algorithms and provide some preliminary but interesting evaluation results. Ontology evolution is an important problem in the Semantic Web research. Recently, Alchourron, Gardenfors and Markinson's (AGM) theory on belief change has been applied to deal with this problem. However, most of current work only focuses on the feasibility of the application of AGM postulates on contraction to description logics (DLs), a family of ontology languages. So the explicit construction of a revision operator is ignored. In this paper, we first generalize the AGM postulates on revision to DLs. We then define two revision operators in DLs. One is the weakening-based revision operator which is defined by weakening of statements in a DL knowledge base and the other is its refinement. We show that both operators capture some notions of minimal change and satisfy the generalized AGM postulates for revision. Belief Revision deals with the problem of adding new information to a knowledge base in a consistent way. Ontology Debugging, on the other hand, aims to find the axioms in a terminological knowledge base which caused the base to become inconsistent. In this article, we propose a belief revision approach in order to find and repair inconsistencies in ontologies represented in some description logic (DL). As the usual belief revision operators cannot be directly applied to DLs, we propose new operators that can be used with more general logics and show that, in particular, they can be applied to the logics underlying OWL-DL and Lite. This paper presents a general, consistency-based framework for expressing belief change. The framework has good formal properties while being well-suited for implementation. For belief revision, informally, in revising a knowledge base K by a sentence α, we begin with α and include as much of K as consistently possible. This is done by expressing K and α in disjoint languages, asserting that the languages agree on the truth values of corresponding atoms wherever consistently possible, and then re-expressing the result in the original language of K. There may be more than one way in which the languages of K and α can be so correlated: in choice revision, one such "extension" represents the revised state; alternately (skeptical) revision consists of the intersection of all such extensions. Contraction is similarly defined although, interestingly, it is not interdefinable with revision.The framework is general and flexible. For example, one could go on and express other belief change operations such as update and erasure, and the merging of knowledge bases. Further, the framework allows the incorporation of static and dynamic integrity constraints. The approach is well-suited for implementation: belief change can be equivalently expressed in terms of a finite knowledge base; and the scope of a belief change operation can be restricted to just those propositions common to the knowledge base and sentence for change. We give a high-level algorithm implementing the procedure, and an expression of the approach in Default Logic. Lastly, we briefly discuss two implementations of the approach.