Semantic Similarities between Objects in Multiple Databases

ions Mappings The structural component Abstraction here refers to the relation between the domains of the two objects Mapping between the domains of objects is the mathematical tool used to express the abstractions However since abstractions by themselves cannot capture the semantic similarity they have to be associated either with the context Kashyap and Sheth or with extra knowledge in order to capture the RWS Some of the proposals are as follows Sheth and Kashyap de ne abstractions in terms of value map pings between the domains of objects and associate it with the context as a part of the semantic proximity Section Ouksel and Naiman de ne mappings between schema elements which they term as inter schema correspondence assertions or ISCAs Section A set of ISCAs under consideration de ne the context for integration of the schemas Sciore et al de ne mappings which they call conversion functions Section which are associated with the meta attributes which de ne the context Yu et al associate the attributes with common concepts Sec tion Thus the mappings relationship between the attributes are determined through the extra knowledge associated with the concepts Garcia Solaco et al upgrade the semantic level of the schemas using abstractions which they call semantic abstractions Section This is achieved as a result of the knowledge acquisition process de scribed in Castellanos Semantic Proximity A model for representing Semantic Similarities Hammer and McLeod discuss an approach for resolving the representa tional di erences which involves a determining as precisely as possible the relationships between sharable objects and b detect possible con icts in their structural representations Modeling Uncertainty Inconsistency and Incompleteness Understanding and representing semantic similaritybetween objects may involve understanding and modeling uncertainty inconsistency and in completeness of the information pertaining to the objects and the relation ships between them modeled in the database both at the intensional and extensional levels Some proposals are as follows Fankhauser et al propose an approach where fuzzy termino logical knowledge is combined with schema knowledge Section to determine semantic similarity Ouksel and Naiman model uncertain information by using the de grees of likelihood of the various intermediate contexts The Dempster Shafer D S theory of belief functions is used to model the likelihood of alternative contexts Section Sheth and Kashyap have used semantic proximity as a basis for representing the uncertainty of the informationmodeled at the database level Section They propose a framework in which the semantic proximity can be mapped to fuzzy strengths comprising the fuzzy ter minological knowledge or to the likelihood of the assertions comprising the context discussed above Yu et al represent each attribute as a vector depending on the concepts associated with it A similaritymeasure between two attributes is de ned as function of the vectors associated with the attributes Semantic Proximity A model for representing Semantic Similarities We recognize three basic aspects in the representation of semantics The rst aspect concentrates on pinning down the real world semantics of the various entities and the relationships between them The second aspect is to Chapter Semantic Similarities between Objects represent all known knowledge about the domain to which the various entities and objects belong The relationships between various objects can then be determined on the basis of the encoded domain knowledge We consider this knowledge itself as an implicit context The nal aspect is when the context is represented explicitly and reasoned about as a rst class construct We distinguish between the real world and the model world which is a representation of the real world See Sheth et al and Garcia Solaco et al for further discussion The term object in this chapter refers to an object in a model world i e a representation or intensional de nition in the model world e g an object class de nition in object oriented models as opposed to an entity or a concept in the real world These objects may model information at any level of representation viz attribute level or entity level We introduce the concept of semantic proximity to characterize semantic similarities between objects and use it to provide a classi cation of semantic similarities between objects Our approach embodies the explicit context rep resentation approach Given two objects O and O the semantic proximity Figure between them is de ned by the tuple given by semPro O O Context Abstraction D D S S where Di is domain of Oi and Si is state of Oi The context of an object is the primary vehicle to capture the RWS of the object Thus the respective contexts of the objects and to a lesser extent the abstraction used to map the domains of the objects help to capture the semantic aspect of the relationship between the two objects Context s of the two Objects the semantic component Each object has its own context The term context in semPro refers to the context in which a particular semantic similarity holds This context may be related to or di erent from the contexts in which the objects were de ned It is possible for two objects to be semantically closer in one context than in another context Some of the alternatives for representing a context in an interoperable database system are as follows In Ouksel and Naiman context is de ned as the knowledge that is needed to reason about another system for the purpose of answering Objects at the entity level can be denoted by single place predicates P x and attributes can be denoted by two place predicates Q x y Sheth and Gala