Domain Definition

In other words, if two domains are equivalent in terms of the set of values they contain, but the description or meaning of the values of at least one element of both domains differs in terms of semantics, should the domains be considered not equivalent?

For example, I could have two equivalent domain defined as follows: Example1

Hence, since DomA and DomB are equivalent as a consequence of the sets of values/elements being subsets of each other.

However, if the domains are extended to incorporate semantic information concerning the values as part of the element definition, then should the domains still be considered equivalent?

If I wanted to extend the definition of Domain A and Domain B above to reflect an extension of semantic representation, I could perhaps use a notation such as the following:
Example2

using a rather informal expression syntax of: 1. <domain_name>={<comma-list of value definitions>} 2. <comma-list of value definitions> =
<elementdef1>,<elementdef2>,...<elementdef-1>,<elementdefn> 3. <elementdef>=<'value':'semantic extension definition'>

Though data/value type could play a part in such scenarios, I am interested in garnering thoughts, opinions, and responses based on the assumption that type (structure, manipulative, and integrity aspects) will be the same across the domains or collection of values (and relations) being compared, and thus would like to isolate the conversion from issues concerning type(s).

Also, for purposes of clarity, assume that the word 'value' is synonymous with value in terms of a type's default representation.

Should a relation (variable) attribute in a heading, identified by the attribute name, act as the 'function' (Chen) that maps any specific value in a domain to proper its semantic extension? If so, that would seem to imply that domains are still equivalent even when equivalent values are regarded as representing something semantically different, such as the case in Example2. This would also lead me to the conclusion that the two domains defined in Example2 would be defined as one domain independent of semantic extension, and that the attribute name mapping function (sometimes also called role) extends any specified value for a tuple to incorporate semantics independent of domain definition.

Also, there seems there could be an major implication in that cases could exist where both attribute names are the same and the domain is the same (same name and collection of value elements), but values map to differing conceptual semantics. Such situations could lead to ambiguity and a lack of clarity in mapping relational elements to conceptual entities and properties.

Which set of relation definitions would be correct provided that the we want to accurately express the semantics of the data from example2 above, but where attribute names are the same:

RelationA=(TransID:Unique_Identifier, Process_Flag:DomA,

                  PK: TransID);
RelationB=(TransID:Unique_Identifier, Process_Flag:DomA
                  PK: TransID);

                  PK:TransID)
RelationB=(TransID:Unique_Identifier, Process_Flag:DomB
                  PK:TransID)

I would also be greatly appreciative if any of you could provide pointers to any academic or industry papers that might provide insight or touch upon this topic.

Thanks In Advance,

Dan Guntermann Received on Thu Jan 09 2003 - 00:17:14 CET