The Ontology Revision

An ontology is a logical theory in an ontology system, which consists of a repre-senting language and deduction rules. In an ontology, classes and individuals organizedhierarchically by the subclass relation between classes and the instance relation betweenindividuals and classes form its main structure. By these two relations, properties can beinherited (defaultly) from classes to their subclasses and instances. For the simplicity ofdiscussion, ontologies are assumed to be trees. Statements in an ontology can be dividedinto four levels: individual level;class level;class-slot level and slot level. Slots are usedto describe classes and individuals. Sub-slots are used to describe slots in order to givevalue restrictions that slots should satisfy when they are used to describe classes or todescribe some certain class. According to the deductive features among statements inthe same level and in di?erent levels, we discuss the deduction mechanism, consistenceand default theories of ontologies.Ontologies provide a very useful way to represent and structure knowledge. However,one of the problems in the development of ontologies is the di?culty in maintainingontologies that face changes. When an ontology accepts new information or knowledge,this new information may contradict with what was described in the ontology. Hence,when this happens, we need to revise the ontology in order to accept new knowledge andto maintain the consistence of the revised ontology. An ontology revision is a process ofchanging an ontology to accommodate a revising statement that is possibly inconsistentwith old statements stated explicitly or implicitly in the ontology.There are two kinds of ontology revision: ontology-set revision and ontology-baserevision. An ontology base is a set of statements that may not be closed under thelogical consequences whereas ontology set is a set of statements closed under the logicalconsequences. We only discuss ontology-base revision.In ontology revision, ontologies are trees and there are logical relations betweenstatements in the same level and in di?erent levels. Hence, besides the principles ofsuccess, consistency and minimal change, other ontology revision postulates, such as thepostulates for the priority order among statements in an ontology, are proposed in orderto preserve the structural features of the revised ontology. Then, according to thesepostulates that the ontology revision should satisfy, a suitable revision method can beselected from multiple revising methods which satisfy the above three principles.To satisfy the postulates of ontology revision, the ontology revision is not only con-tracting ontologies by discarding statements inconsistent with a revising statement whenthe revising statement is inconsistent with the ontologies, but also adding statementsother than the revising statement. Moreover, when statements in slot level or class-slotlevel are extracted from an ontology, they are modified and added back to the revisedontology.The existing approach to belief revision is to provide a set of postulates for beliefrevision functions such as the AGM postulates and the DP postulates. These postulatesconstrain what revision functions should satisfy in the process of revision. Similar to beliefrevision, we study ontology revision by proposing a set of axioms for ontology revisionfunctions and based on these axioms, we give a concrete ontology revision operator.To formally compare ontology revision with belief revision, we give a translationfunction from an ontology system to default logic, and discuss its features. According tothe structural features and deduction mechanism of ontologies, we translate the logicalclosure of an ontology, but not the ontology to a default theory. Based on the translationfrom an ontology system to default logic and the ontology revision operator, we definea belief revision operator to revise the default theory, and compare the belief revisionoperator with the ontology revision operator formally. Finally, we analyze the distinctionbetween these two operators intuitively through examples.The main results of this dissertation consist of the following four parts:(1) Giving the language and deduction rules of an ontology system and the formaldefinition of an ontology. According to con?icts among statements in the same level andin di?erent levels, the consistence of an ontology and of the logical closure of the ontologyis discussed. Finally, an ontology is translated into a default theory of an ontology system,which is proved to have a unique extension.(2) Proposing six ontology revision postulates based on the structural propertiesof an ontology and the logical relations between statements. These six postulates arethe postulate of satisfying the principles of success, consistency and minimal change;the reclassification postulate, the postulate of an ontology, a revising statement and therevised ontology;the postulate of changing the structure of an ontology;the postulateof the priority order among statements;and the postulate of modifying statements inan ontology. In terms of the ontological assumptions and the postulates of the ontologyrevision that a revised ontology should satisfy, an OR axiom system for the ontologyrevision which imply the principles of success and consistency is given.(3) Developing a concrete ontology revision operator satisfying the revision postu-lates, according to the consistence of a revising statement with an ontology, with thelogical closure of the ontology and with the extended theory of the logical closure of theontology under the closed world assumption. The operator is proved to satisfy the ORaxiom system.(4) Giving a translation function from an ontology system to default logic and dis-cussing the features of this function. Based on this function and the ontology revisionoperator, a belief revision operator to revise the default theory translated from an on-tology is defined and proved to satisfy the AGM postulates and the BR axiom systemtranslated from the OR axiom system.