Mappings RDB Ontology Ankesh

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• Question is for the Presentation: Joshua Taylor presents Discovering Simple Mappings Between Relational Database Schemas and Ontologies
• Question is asked by: Ankesh Khandelwal
• The Question is:

1. In section 4.1 the paper says n-arity relationship should be reified as a group of binary relationships. I couldn't create a clear picture how this would be done, especially what would the namings of the relations be. Would it be the attribute name that is not part of primary key? What does reified mean here? How would tokens be affected?
2. In section 4.3, paper validates relationship between attribute id in author and hasID in ontology. I couldn't understand why would they be mapped in first place? Because from (2) VD(id) would contain Des(author) where as from (4) VD(hasID) would contain Des(Paper). What is confident mapping (good confidence measure)? Could you help with a better example for validation?
3. In section 4.4, the algorithm distinguishes categorical attribute to non-categorical. However, it isn't clear to me how do we determine if an attribute is categorical? A naive description can be any attribute not part of primary key is categorical. Can this be correct?

• Question answered by: Joshua Taylor
• Answer:

1. An example from Wikipedia, particularly http://en.wikipedia.org/wiki/Relation_(mathematics) :

   An example of a ternary or triadic relation (i.e., between three individuals) is: "X was-introduced-to Y by Z", where (X,Y,Z) is a 3-tuple of persons; for example, "Beatrice Wood was-introduced-to Henri-Pierre Roché by Marcel Duchamp" is true, while "Karl Marx was-introduced-to Friedrich Engels by Queen Victoria" is false.

   This (somewhat contrived) relation could be represented using a relational database. It would be a "relationship relation", and each row would store an X, a Y, and a Z. In order to represent this relationship using a triple based model, it is necessary to introduce some sort of "introducing event" objects which correspond to the rows of the table, and which would be the domain of three properties, say, introduction_event:person1, introduction_event:person2, and introduction_event:introducer. A similar thing has to happen if the database contains a Person table with three attributes, name, birthdate, and gender; the difference is that it does not seem strange to us to introduce Person objects—they're just people.
2. The authors are using this example to show how the validation process would eliminate an inconsistent mapping. (Their language is a bit unclear, though.) Presumably the mapping between hasID and id would be discovered based on the results of Des(hasID) and Des(id). Though in this example "hasID" and "id" are distinct tokens, they might, in reality, have some more complex descriptions which have some similarity. If this isn't the case, it is hard to imagine the authors' system overcoming any lexical differences in terminologies that arise between databases and ontologies.
3. Immediately below 'ContextMatch, the authors write "In lines 6–8, the algorithm repeatedly examines each attribute in the relation ((to determine)) whether it is a categorical attribute or not." Based on the way that they use the categorical attributes, a categorical attribute is one in which a partitioning of instances based on their attribute values corresponds to some partitioning of the disjoint subclasses of the class at hand.