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.
In this paper I used reinterpretation operators as change operators on ontologies described in DLs. There are different other approaches that use the ideas of belief revision for different forms of ontology change such as ontology evolution over DL-Lite ontologies @cite_1 or ontology debugging @cite_20 . As the consequence operator over DLs do not fulfill all preconditions assumed by AGM @cite_13 one cannot directly transfer AGM constructions and ideas one-to-one to the DL setting as noted, e.g., by Flouris and colleagues @cite_11 and dealt in more depth for non-classical logics by Ribeiro @cite_19 . For the definition of the reinterpretation operators the constraint is not essential. Nonetheless, they lead to constraints in providing appropriate counter examples: namely ontologies expressible in the DL at hand.
@cite_1 @cite_19 @cite_13 @cite_20 @cite_11
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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. Many real-world knowledge-based systems must deal with information coming from different sources that invariably leads to incompleteness, overspecification, or inherently uncertain content. The presence of these varying levels of uncertainty doesn't mean that the information is worthless --- rather, these are hurdles that the knowledge engineer must learn to work with. In this paper, we continue work on an argumentation-based framework that extends the well-known Defeasible Logic Programming (DeLP) language with probabilistic uncertainty, giving rise to the Defeasible Logic Programming with Presumptions and Probabilistic Environments (DeLP3E) model. Our prior work focused on the problem of belief revision in DeLP3E, where we proposed a non-prioritized class of revision operators called AFO (Annotation Function-based Operators) to solve this problem. In this paper, we further study this class and argue that in some cases it may be desirable to define revision operators that take quantitative aspects into account, such as how the probabilities of certain literals or formulas of interest change after the revision takes place. To the best of our knowledge, this problem has not been addressed in the argumentation literature to date. We propose the QAFO (Quantitative Annotation Function-based Operators) class of operators, a subclass of AFO, and then go on to study the complexity of several problems related to their specification and application in revising knowledge bases. Finally, we present an algorithm for computing the probability that a literal is warranted in a DeLP3E knowledge base, and discuss how it could be applied towards implementing QAFO-style operators that compute approximations rather than exact operations. In this paper, we present a semantical approach to multi-agent belief revision and belief update. For this, we introduce relational structures called conditional doxastic models (CDM's, for short). We show this setting to be equivalent to an epistemic version of the classical AGM Belief Revision theory. We present a logic of conditional beliefs that is complete w.r.t. CDM's. Moving then to belief updates (sometimes called ''dynamic'' belief revision) induced by epistemic actions, we consider two particular cases: public announcements and private announcements to subgroups of agents. We show how the standard semantics for these types of updates can be appropriately modified in order to apply it to CDM's, thus incorporating belief revision into our notion of update. We provide a complete axiomatization of the corresponding dynamic doxastic logics. As an application, we solve a ''cheating version'' of the Muddy Children Puzzle.