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.
Evolution of Knowledge Bases (KBs) expressed in Description Logics (DLs) has gained a lot of attention lately. Recent studies on the topic have mostly focused on so-called model-based approaches (MBAs), where the evolution of a KB results in a set of models. For KBs expressed in tractable DLs, such as those of the DL-Lite family, which we consider here, it has been shown that one faces inexpressibility of evolution, i.e., the result of evolution of a DL-Lite KB in general cannot be expressed in DL-Lite, in other words, DL-Lite is not closed under evolution. What is still missing in these studies is a thorough understanding of various important aspects of the evolution problem for DL-Lite KBs: Which fragments of DL-Lite are closed under evolution? What causes the inexpressibility? Can one approximate evolution in DL-Lite, and if yes, how? This work provides some understanding of these issues for an important class of MBAs, which cover the cases of both update and revision. We describe what causes inexpressibility, and we propose techniques (based on what we call prototypes) that help to approximate evolution under the well-known approach by Winslett, which is inexpressible in DL-Lite. We also identify a fragment of DL-Lite closed under evolution, and for this fragment we provide polynomial-time algorithms to compute or approximate evolution results for various MBAs. In this article, we propose a belief revision approach for families of (non-classical) logics whose semantics are first-order axiomatisable. Given any such (non-classical) logic , the approach enables the definition of belief revision operators for , in terms of a belief revision operation satisfying the postulates for revision theory proposed by Alchourron, Gardenfors and Makinson (AGM revision, (1985)). The approach is illustrated by considering the modal logic K , Belnap's four-valued logic, and Łukasiewicz's many-valued logic. In addition, we present a general methodology to translate algebraic logics into classical logic. For the examples provided, we analyse in what circumstances the properties of the AGM revision are preserved and discuss the advantages of the approach from both theoretical and practical viewpoints. This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate “partial meet contraction functions”, which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are “relational” and “transitively relational”, are studied in detail, and their connections with certain “supplementary postulates” of Gardenfors investigated, with a further representation theorem established. 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. 